I've never had this happen but I'm in a longarm guild and this issue was addressed at a meeting.
One longarmer had an interesting solution. She set her regular domestic sewing machine on the table where pantos go. She removed only pins at the bottom of the quilt, pinned on another piece of fabric, and sewed it to the bottom of the backing WITHOUT REMOVING THE QUILT FROM THE LONGARM. She simply pulled it to the back table and sewed the extra fabric on, then re-attached the backing to the belly bar with the new strip sewn on.
Well, another longarmer did her one better by telling us he did the same but not with his domestic machine. He sewed the extra strip on WITH THE LONGARM. Some people are just so creative.