A point of clarification / caution....(something I learned the "hard way")
Sebastian is correct if you use DNN File Manager or some other DNN-aware file management interface to move files around.
 
If, however, you move files manually via some tool external to DNN (FTP, Windows Explorer, etc) your FileID references will still break.  Further, upon next complete file synch you will also lose your old FileID references (in the database table FILES) as the moved files will no longer be found by DNN in the expected locations and the DB table entries will be removed (deleted, not deactivated).  After this happens the links won't work even if you move the files back to their original locations -- in that event, upon file synch DNN will see the files as "new files" and assign them new file ID values.  It can be a vicious scenario when you're not expecting it.
 
-mamlin