If you open a document such as ~/Documents/foo.odt and then later delete or rename that document while LibreOffice is not running, when you open LibreOffice it will still show up in "File > Recent Documents", the Open button's dropdown list button, etc. It shouldn't...
i think this issue is a duplicate of:
Bug 101302 - Deleted files visible as recent documents in menu and start center
If you disagree, please leave a comment.
*** This bug has been marked as a duplicate of bug 101302 ***