I wouldn't expect Foobar, or any other program, to lose files due to an aborted or crashed copy operation. The normal procedure when a program moves files is to write the file to the new location before deleting the original. That way if the copy process crashes or is aborted then nothing is lost.
Maybe the files are in limbo in a temp directory somewhere?
Many playlist formats, like M3U, have the song locations hard-coded. If you move the files the playlist will no longer be pointing to the files. The playlist will still be pointing to the old location. Could that be the problem? I don't know if Foobar rewrites the playlist file to point to the new location when it moves files.