diff --git a/dvc/ignore.py b/dvc/ignore.py
--- a/dvc/ignore.py
+++ b/dvc/ignore.py
@@ -5,7 +5,9 @@
 from pathspec import PathSpec
 from pathspec.patterns import GitWildMatchPattern
 
+from dvc.path_info import PathInfo
 from dvc.scm.tree import BaseTree
+from dvc.utils import relpath
 
 logger = logging.getLogger(__name__)
 
@@ -125,19 +127,79 @@ def tree_root(self):
         return self.tree.tree_root
 
     def open(self, path, mode="r", encoding="utf-8"):
-        return self.tree.open(path, mode, encoding)
+        if self.isfile(path):
+            return self.tree.open(path, mode, encoding)
+        raise FileNotFoundError
 
     def exists(self, path):
-        return self.tree.exists(path)
+        if self.tree.exists(path) and self._parents_exist(path):
+            if self.tree.isdir(path):
+                return self._valid_dirname(path)
+            return self._valid_filename(path)
+        return False
 
     def isdir(self, path):
-        return self.tree.isdir(path)
+        return (
+            self.tree.isdir(path)
+            and self._parents_exist(path)
+            and self._valid_dirname(path)
+        )
+
+    def _valid_dirname(self, path):
+        dirname, basename = os.path.split(os.path.normpath(path))
+        dirs, _ = self.dvcignore(os.path.abspath(dirname), [basename], [])
+        if dirs:
+            return True
+        return False
 
     def isfile(self, path):
-        return self.tree.isfile(path)
+        return (
+            self.tree.isfile(path)
+            and self._parents_exist(path)
+            and self._valid_filename(path)
+        )
+
+    def _valid_filename(self, path):
+        dirname, basename = os.path.split(os.path.normpath(path))
+        _, files = self.dvcignore(os.path.abspath(dirname), [], [basename])
+        if files:
+            return True
+        return False
 
     def isexec(self, path):
-        return self.tree.isexec(path)
+        return self.exists(path) and self.tree.isexec(path)
+
+    def _parents_exist(self, path):
+        from dvc.repo import Repo
+
+        path = PathInfo(path)
+
+        # if parent is tree_root or inside a .dvc dir we can skip this check
+        if path.parent == self.tree_root or Repo.DVC_DIR in path.parts:
+            return True
+
+        # if path is outside of tree, assume this is a local remote/local cache
+        # link/move operation where we do not need to filter ignores
+        path = relpath(path, self.tree_root)
+        if path.startswith("..") or (
+            os.name == "nt"
+            and not os.path.commonprefix(
+                [os.path.abspath(path), self.tree_root]
+            )
+        ):
+            return True
+
+        # check if parent directories are in our ignores, starting from
+        # tree_root
+        for parent_dir in reversed(PathInfo(path).parents):
+            dirname, basename = os.path.split(parent_dir)
+            if basename == ".":
+                # parent_dir == tree_root
+                continue
+            dirs, _ = self.dvcignore(os.path.abspath(dirname), [basename], [])
+            if not dirs:
+                return False
+        return True
 
     def walk(self, top, topdown=True):
         for root, dirs, files in self.tree.walk(top, topdown):
@@ -148,4 +210,6 @@ def walk(self, top, topdown=True):
             yield root, dirs, files
 
     def stat(self, path):
-        return self.tree.stat(path)
+        if self.exists(path):
+            return self.tree.stat(path)
+        raise FileNotFoundError

Ok, so discussed with @pmrowla and @pared that it makes sense to forbid it. If someone asks for this in the future, we could introduce `--subrepos` or smth like that for push/pull/etc.
The reason it does't throw an error right now is https://github.com/iterative/dvc/blob/1.0.0a1/dvc/repo/__init__.py#L210 . It opens dvcfile directly without consulting with the clean tree.

As discovered by @skshetry , repo.tree doesn't use dvcignore when checking if something exists (only uses it when walk()ing). So we need to revisit CleanTree to fix that.
diff --git a/tests/func/test_tree.py b/tests/func/test_tree.py
--- a/tests/func/test_tree.py
+++ b/tests/func/test_tree.py
@@ -3,6 +3,7 @@
 
 from dvc.ignore import CleanTree
 from dvc.path_info import PathInfo
+from dvc.repo import Repo
 from dvc.repo.tree import RepoTree
 from dvc.scm import SCM
 from dvc.scm.git import GitTree
@@ -220,3 +221,23 @@ def test_repotree_cache_save(tmp_dir, dvc, scm, erepo_dir, setup_remote):
             cache.save(PathInfo(erepo_dir / "dir"), None, tree=tree)
     for checksum in expected:
         assert os.path.exists(cache.checksum_to_path_info(checksum))
+
+
+def test_cleantree_subrepo(tmp_dir, dvc, scm, monkeypatch):
+    tmp_dir.gen({"subdir": {}})
+    subrepo_dir = tmp_dir / "subdir"
+    with subrepo_dir.chdir():
+        subrepo = Repo.init(subdir=True)
+        subrepo_dir.gen({"foo": "foo", "dir": {"bar": "bar"}})
+
+    assert isinstance(dvc.tree, CleanTree)
+    assert not dvc.tree.exists(subrepo_dir / "foo")
+    assert not dvc.tree.isfile(subrepo_dir / "foo")
+    assert not dvc.tree.exists(subrepo_dir / "dir")
+    assert not dvc.tree.isdir(subrepo_dir / "dir")
+
+    assert isinstance(subrepo.tree, CleanTree)
+    assert subrepo.tree.exists(subrepo_dir / "foo")
+    assert subrepo.tree.isfile(subrepo_dir / "foo")
+    assert subrepo.tree.exists(subrepo_dir / "dir")
+    assert subrepo.tree.isdir(subrepo_dir / "dir")

forbid using subrepo as a target
**Please provide information about your setup**
DVC version(i.e. `dvc --version`), Platform and method of installation (pip, homebrew, pkg Mac, exe (Windows), DEB(Linux), RPM(Linux))

After introducing support for multiple DVC roots in #3257, in case of following setup:
```
.
├── .dvc
├── .git
└── subrepo
    ├── data
    ├── data.dvc
    ├── .dvc
    └── .gitignore
```
Running command `dvc push/pull/fetch subrepo/data.dvc` will have some unexpected results.
Eg. push will push to remote stored in parent repo. 
The reason for that is that we are not resolving Repo basing on `target`, but `cwd`. 
To solve this, we should either forbid initializing `Repo` under other `Repo`, or implement dynamic resolving of target paths. 
Other commands that need to be checked for this issue:
`destroy`, `remove`, `move`, `repro`, `status`, `import`, `get`, `root`, `update`, `pipeline`.

As simply forbidding seems like easier way, we will probably need to solve this problem anyway, to support `import` and  `get`.

Related to https://github.com/iterative/dvc.org/pull/1022

tests/func/test_tree.py::test_cleantree_subrepo
tests/func/test_tree.py::TestGitTree::test_isfile tests/func/test_tree.py::TestWorkingTree::test_isdir tests/func/test_tree.py::TestGitSubmoduleTree::test_isdir tests/func/test_tree.py::TestWalkInGit::test_nobranch tests/func/test_tree.py::TestWalkInGit::test_branch tests/func/test_tree.py::TestGitTree::test_exists tests/func/test_tree.py::TestGitTree::test_isdir tests/func/test_tree.py::TestWalkInNoSCM::test_subdir tests/func/test_tree.py::TestGitSubmoduleTree::test_exists tests/func/test_tree.py::TestWalkInNoSCM::test tests/func/test_tree.py::TestGitTree::test_open tests/func/test_tree.py::TestGitSubmoduleTree::test_open tests/func/test_tree.py::TestWorkingTree::test_open tests/func/test_tree.py::TestGitSubmoduleTree::test_isfile tests/func/test_tree.py::TestWorkingTree::test_exists tests/func/test_tree.py::TestWorkingTree::test_isfile