Something similar happen to a friend. The longarmer told her she was short of fabric, so she sent over some extra fabric of the backing and of some of the front piecing fabric. I guess it was miscommunication, because the longarmer used the front fabric to add to the backing and turned the quilt back to her along with the unused extra backing. My friend's solution was to hand sew the extra backing over the whole length of the finished pieced area. She then hand quilted it from the back side just going through a few layers and matching stitch locations to the machine quilting on the front. Nobody is the wiser, and my friend is happy, although it took a bit of work.