diff --git a/dvc/command/add.py b/dvc/command/add.py
--- a/dvc/command/add.py
+++ b/dvc/command/add.py
@@ -18,6 +18,7 @@ def run(self):
                 recursive=self.args.recursive,
                 no_commit=self.args.no_commit,
                 fname=self.args.file,
+                external=self.args.external,
             )
 
         except DvcException:
@@ -49,6 +50,12 @@ def add_parser(subparsers, parent_parser):
         default=False,
         help="Don't put files/directories into cache.",
     )
+    parser.add_argument(
+        "--external",
+        action="store_true",
+        default=False,
+        help="Allow targets that are outside of the DVC repository.",
+    )
     parser.add_argument(
         "-f",
         "--file",
diff --git a/dvc/command/run.py b/dvc/command/run.py
--- a/dvc/command/run.py
+++ b/dvc/command/run.py
@@ -53,6 +53,7 @@ def run(self):
                 always_changed=self.args.always_changed,
                 name=self.args.name,
                 single_stage=self.args.single_stage,
+                external=self.args.external,
             )
         except DvcException:
             logger.exception("")
@@ -225,6 +226,12 @@ def add_parser(subparsers, parent_parser):
         default=False,
         help=argparse.SUPPRESS,
     )
+    run_parser.add_argument(
+        "--external",
+        action="store_true",
+        default=False,
+        help="Allow outputs that are outside of the DVC repository.",
+    )
     run_parser.add_argument(
         "command", nargs=argparse.REMAINDER, help="Command to execute."
     )
diff --git a/dvc/repo/add.py b/dvc/repo/add.py
--- a/dvc/repo/add.py
+++ b/dvc/repo/add.py
@@ -21,7 +21,9 @@
 
 @locked
 @scm_context
-def add(repo, targets, recursive=False, no_commit=False, fname=None):
+def add(
+    repo, targets, recursive=False, no_commit=False, fname=None, external=False
+):
     if recursive and fname:
         raise RecursiveAddingWhileUsingFilename()
 
@@ -52,7 +54,9 @@ def add(repo, targets, recursive=False, no_commit=False, fname=None):
                     )
                 )
 
-            stages = _create_stages(repo, sub_targets, fname, pbar=pbar)
+            stages = _create_stages(
+                repo, sub_targets, fname, pbar=pbar, external=external
+            )
 
             try:
                 repo.check_modified_graph(stages)
@@ -120,7 +124,7 @@ def _find_all_targets(repo, target, recursive):
     return [target]
 
 
-def _create_stages(repo, targets, fname, pbar=None):
+def _create_stages(repo, targets, fname, pbar=None, external=False):
     from dvc.stage import Stage, create_stage
 
     stages = []
@@ -132,7 +136,14 @@ def _create_stages(repo, targets, fname, pbar=None):
         unit="file",
     ):
         path, wdir, out = resolve_paths(repo, out)
-        stage = create_stage(Stage, repo, fname or path, wdir=wdir, outs=[out])
+        stage = create_stage(
+            Stage,
+            repo,
+            fname or path,
+            wdir=wdir,
+            outs=[out],
+            external=external,
+        )
         if stage:
             Dvcfile(repo, stage.path).remove_with_prompt(force=True)
 
diff --git a/dvc/stage/__init__.py b/dvc/stage/__init__.py
--- a/dvc/stage/__init__.py
+++ b/dvc/stage/__init__.py
@@ -19,6 +19,7 @@
     check_circular_dependency,
     check_duplicated_arguments,
     check_missing_outputs,
+    check_no_externals,
     check_stage_path,
     compute_md5,
     fill_stage_dependencies,
@@ -52,7 +53,7 @@ def loads_from(cls, repo, path, wdir, data):
     return cls(**kw)
 
 
-def create_stage(cls, repo, path, **kwargs):
+def create_stage(cls, repo, path, external=False, **kwargs):
     from dvc.dvcfile import check_dvc_filename
 
     wdir = os.path.abspath(kwargs.get("wdir", None) or os.curdir)
@@ -63,6 +64,8 @@ def create_stage(cls, repo, path, **kwargs):
 
     stage = loads_from(cls, repo, path, wdir, kwargs)
     fill_stage_outputs(stage, **kwargs)
+    if not external:
+        check_no_externals(stage)
     fill_stage_dependencies(
         stage, **project(kwargs, ["deps", "erepo", "params"])
     )
diff --git a/dvc/stage/cache.py b/dvc/stage/cache.py
--- a/dvc/stage/cache.py
+++ b/dvc/stage/cache.py
@@ -102,6 +102,7 @@ def _create_stage(self, cache, wdir=None):
             params=params,
             deps=[dep["path"] for dep in cache.get("deps", [])],
             outs=[out["path"] for out in cache["outs"]],
+            external=True,
         )
         StageLoader.fill_from_lock(stage, cache)
         return stage
diff --git a/dvc/stage/exceptions.py b/dvc/stage/exceptions.py
--- a/dvc/stage/exceptions.py
+++ b/dvc/stage/exceptions.py
@@ -58,6 +58,10 @@ class StageCommitError(DvcException):
     pass
 
 
+class StageExternalOutputsError(DvcException):
+    pass
+
+
 class StageUpdateError(DvcException):
     def __init__(self, path):
         super().__init__(
diff --git a/dvc/stage/utils.py b/dvc/stage/utils.py
--- a/dvc/stage/utils.py
+++ b/dvc/stage/utils.py
@@ -6,9 +6,10 @@
 from dvc.utils.fs import path_isin
 
 from ..remote import LocalRemote, S3Remote
-from ..utils import dict_md5, relpath
+from ..utils import dict_md5, format_link, relpath
 from .exceptions import (
     MissingDataSource,
+    StageExternalOutputsError,
     StagePathNotDirectoryError,
     StagePathNotFoundError,
     StagePathOutsideError,
@@ -68,6 +69,31 @@ def fill_stage_dependencies(stage, deps=None, erepo=None, params=None):
     stage.deps += dependency.loads_params(stage, params or [])
 
 
+def check_no_externals(stage):
+    from urllib.parse import urlparse
+
+    # NOTE: preventing users from accidentally using external outputs. See
+    # https://github.com/iterative/dvc/issues/1545 for more details.
+
+    def _is_external(out):
+        # NOTE: in case of `remote://` notation, the user clearly knows that
+        # this is an advanced feature and so we shouldn't error-out.
+        if out.is_in_repo or urlparse(out.def_path).scheme == "remote":
+            return False
+        return True
+
+    outs = [str(out) for out in stage.outs if _is_external(out)]
+    if not outs:
+        return
+
+    str_outs = ", ".join(outs)
+    link = format_link("https://dvc.org/doc/user-guide/managing-external-data")
+    raise StageExternalOutputsError(
+        f"Output(s) outside of DVC project: {str_outs}. "
+        f"See {link} for more info."
+    )
+
+
 def check_circular_dependency(stage):
     from dvc.exceptions import CircularDependencyError
 

This is just a usual "external output" case, where you want to extend your project's workspace with the workspace of your entire machine. I don't think it is a bug, but rather a miscommunication. I guess people expect `dvc add` to copy a file to their project? 
The guy saw `dvc add` command and interpreted that as adding a file under DVC control. The dataset was deleted from the external drive after the project was deleted.

I expect this `dvc add external-file` scenario is quite common and we should do something about this. The external output scenario might be a good one but we should think more carefully about this scenario and how it intersects with the basic scenario. I'll think about the intersection and I'll try to propose some solution.
@dmpetrov I see, this is the guy from ODS you are talking about. Agreed. I think we could simply add a confirmation prompt for external local files along with something like `--external` flag to suppress it. Will take a closer look at this later.
Yeah, that's what I was thinking about. But let's think a bit more about this experience.
Or, as discussed with @shcheklein , we could require a special external cache setup for external outputs, same as we do with s3/gs/etc. That way it would error-out automatically, without us having to introduce --external flag, that is breaking the symmetry for s3/gs/etc external outputs.
More context on this - https://discuss.dvc.org/t/share-nas-data-in-server/180 . It looks it's a really common thing and the way our "external outputs" behave in this case is very confusing.
The scenario with external outputs makes seen but it is too advanced for `dvc add` and it confuses people and especially beginners. This is a usual error in the first-day experience no matter what is the user's background - hardcore users can easily make this mistake.

Let's prevent using external outputs in `dvc add`. Advanced users can use  `dvc run -o ~/Download/myfile` (no command) instead of `dvc add ~/Download/myfile`.
It is also related to #2955. DVC needs to resolve paths, exits with an error if the path is outside the current repo (no external outputs). The paths inside the repo need to be converted to relevant paths.
Had a great discussion with @dmpetrov and @shcheklein that it might make sense to introduce a config option instead of `--external` for now, as it will be much less annoying to the advanced users.

But a proper solution here, is probably to introduce a notion of workspaces, that will enforce proper use. E.g. maybe something like
```
dvc workspace add mys3 s3://bucket/ruslan  # this might even automatically create .dvc/cache, similar to local workspace
dvc add s3://bucket/ruslan/path # will understand that the file is within the legal workspace
```
but it should carefully evaluated. We will do that later. For now we need to prevent new users from shooting themselves in the leg.
diff --git a/tests/func/test_add.py b/tests/func/test_add.py
--- a/tests/func/test_add.py
+++ b/tests/func/test_add.py
@@ -187,11 +187,16 @@ def test_add_file_in_dir(tmp_dir, dvc):
 
 class TestAddExternalLocalFile(TestDvc):
     def test(self):
+        from dvc.stage.exceptions import StageExternalOutputsError
+
         dname = TestDvc.mkdtemp()
         fname = os.path.join(dname, "foo")
         shutil.copyfile(self.FOO, fname)
 
-        stages = self.dvc.add(fname)
+        with self.assertRaises(StageExternalOutputsError):
+            self.dvc.add(fname)
+
+        stages = self.dvc.add(fname, external=True)
         self.assertEqual(len(stages), 1)
         stage = stages[0]
         self.assertNotEqual(stage, None)
diff --git a/tests/func/test_gc.py b/tests/func/test_gc.py
--- a/tests/func/test_gc.py
+++ b/tests/func/test_gc.py
@@ -153,7 +153,7 @@ def test(self):
         cwd = os.getcwd()
         os.chdir(self.additional_path)
         # ADD FILE ONLY IN SECOND PROJECT
-        fname = os.path.join(self.additional_path, "only_in_second")
+        fname = "only_in_second"
         with open(fname, "w+") as fobj:
             fobj.write("only in additional repo")
 
@@ -161,7 +161,7 @@ def test(self):
         self.assertEqual(len(stages), 1)
 
         # ADD FILE IN SECOND PROJECT THAT IS ALSO IN MAIN PROJECT
-        fname = os.path.join(self.additional_path, "in_both")
+        fname = "in_both"
         with open(fname, "w+") as fobj:
             fobj.write("in both repos")
 
diff --git a/tests/func/test_get.py b/tests/func/test_get.py
--- a/tests/func/test_get.py
+++ b/tests/func/test_get.py
@@ -101,7 +101,8 @@ def test_get_full_dvc_path(tmp_dir, erepo_dir, tmp_path_factory):
     external_data.write_text("ext_data")
 
     with erepo_dir.chdir():
-        erepo_dir.dvc_add(os.fspath(external_data), commit="add external data")
+        erepo_dir.dvc.add(os.fspath(external_data), external=True)
+        erepo_dir.scm_add("ext_data.dvc", commit="add external data")
 
     Repo.get(
         os.fspath(erepo_dir), os.fspath(external_data), "ext_data_imported"
diff --git a/tests/func/test_repro.py b/tests/func/test_repro.py
--- a/tests/func/test_repro.py
+++ b/tests/func/test_repro.py
@@ -963,6 +963,7 @@ def test(self, mock_prompt):
             deps=[out_foo_path],
             cmd=self.cmd(foo_path, bar_path),
             name="external-base",
+            external=True,
         )
 
         self.assertEqual(self.dvc.status([cmd_stage.addressing]), {})
diff --git a/tests/unit/command/test_run.py b/tests/unit/command/test_run.py
--- a/tests/unit/command/test_run.py
+++ b/tests/unit/command/test_run.py
@@ -39,6 +39,7 @@ def test_run(mocker, dvc):
             "file:param1,param2",
             "--params",
             "param3",
+            "--external",
             "command",
         ]
     )
@@ -70,6 +71,7 @@ def test_run(mocker, dvc):
         cmd="command",
         name="nam",
         single_stage=False,
+        external=True,
     )
 
 
@@ -99,6 +101,7 @@ def test_run_args_from_cli(mocker, dvc):
         cmd="echo foo",
         name=None,
         single_stage=False,
+        external=False,
     )
 
 
@@ -128,4 +131,5 @@ def test_run_args_with_spaces(mocker, dvc):
         cmd='echo "foo bar"',
         name=None,
         single_stage=False,
+        external=False,
     )
diff --git a/tests/unit/stage/test_stage.py b/tests/unit/stage/test_stage.py
--- a/tests/unit/stage/test_stage.py
+++ b/tests/unit/stage/test_stage.py
@@ -102,3 +102,21 @@ def test_always_changed(dvc):
     with dvc.lock:
         assert stage.changed()
         assert stage.status()["path"] == ["always changed"]
+
+
+def test_external_outs(tmp_path_factory, dvc):
+    from dvc.stage import create_stage
+    from dvc.stage.exceptions import StageExternalOutputsError
+
+    tmp_path = tmp_path_factory.mktemp("external-outs")
+    foo = tmp_path / "foo"
+    foo.write_text("foo")
+
+    with pytest.raises(StageExternalOutputsError):
+        create_stage(Stage, dvc, "path.dvc", outs=[os.fspath(foo)])
+
+    with dvc.config.edit() as conf:
+        conf["remote"]["myremote"] = {"url": os.fspath(tmp_path)}
+
+    create_stage(Stage, dvc, "path.dvc", outs=["remote://myremote/foo"])
+    create_stage(Stage, dvc, "path.dvc", outs=[os.fspath(foo)], external=True)

add: from external FS or local external outputs
```
$ dvc add /Volumes/Seagate/storage/data/reddit-May2015_z.tsv.zip
```
It copies the file into the cache, removes the original file in the external drive and creates symlink instead (to the dvc cache).

Based on some offline discussions it confuses people. One of the biggest concerns - after removing DVC project (the entire dir with the code as well as DVC-cache) user sees a symlink to a file which does not exist.

1. Why should DVC work with external files? Is there any meaningful scenario? If not - let's throw an error when adding external files.
2. Even if we have a scenario for (1) let's not touch\remove external files?
3. As a result of the command, I have `reddit-May2015_z.tsv.zip.dvc` file but not the actual file in the workspace (like `reddit-May2015_z.tsv.zip`). It is not clear how to instantiate the file in the workspace?


tests/unit/stage/test_stage.py::test_external_outs tests/unit/command/test_run.py::test_run_args_from_cli tests/unit/command/test_run.py::test_run tests/unit/command/test_run.py::test_run_args_with_spaces
tests/func/test_gc.py::test_gc_without_workspace_on_tags_branches_commits tests/unit/stage/test_stage.py::test_wdir_non_default_is_not_ignored tests/unit/stage/test_stage.py::test_wdir_default_ignored tests/func/test_get.py::test_get_git_dir tests/func/test_gc.py::test_gc_without_workspace_raises_error tests/func/test_gc.py::test_gc_cloud_without_any_specifier tests/func/test_get.py::test_unknown_path tests/func/test_get.py::test_absolute_file_outside_git_repo tests/unit/stage/test_stage.py::test_stage_checksum tests/func/test_gc.py::test_gc_without_workspace tests/func/test_get.py::test_get_url_git_only_repo tests/func/test_get.py::test_get_git_file tests/func/test_gc.py::test_gc_cloud_positive tests/func/test_get.py::test_absolute_file_outside_repo tests/unit/stage/test_stage.py::TestPathConversion::test tests/unit/stage/test_stage.py::test_meta_ignored tests/unit/stage/test_stage.py::test_stage_update tests/func/test_get.py::test_get_url_not_existing tests/func/test_gc.py::test_gc_with_possible_args_positive tests/func/test_get.py::test_get_a_dvc_file tests/unit/stage/test_stage.py::test_always_changed tests/func/test_gc.py::test_gc_cloud_with_or_without_specifier tests/func/test_get.py::test_get_from_non_dvc_repo