If the corners are really tattered, you might have to cut them off. If so, I'd cut the old binding off and round the corners for a new look. Funny this should come up today as I'm about to help a non-quilting friend tie a quilt. She made the top years ago and says she wants to finish it. I suggested she send it to be long armed, but she wants to claim she made it all by herself. I'm curious about what shape it will be in but am willing to help.