Peter,
I just tried this and it did work for me.
I linked a text file, moved its location so it had a missing link icon, enabled LINKING in Preferences and had the UNLINK drop down menu item available. Clicked Unlink, the text vanished from the Link menu and remained embedded in the text box. Worked like a charm.
I also would like the OP to try this on his doc (preferable a copy for safety). Couldn't hurt.