How to recover TextEdit files?
If you quit TextEdit, then reopening TextEdit will re-open all your documents. If it didn't give you an option to save, then they were stored by Restore in the Saved Application State. When you next open the app, they should have been there as the application state is restored. If this did not occur, then something else went wrong and the application state was either not saved or not restored correctly (e.g. force quit whilst opening will cancel restoration of application state).

If you closed TextEdit, then all the documents will be closed, and clicking Don't Save will delete them and you will not be able to recover them.