Are you planning to take the entire quilt apart? If so, maybe a very light weight fusible stabilizer would help. It would make it a bit stiffer, and then with new batting and depending on the pattern of the front fabric decide to quilt the whole thing or tie it. I can't imagine that if you just sewed the 2 fabrics together it wouldn't help the older fabric very much. Maybe the owner of the quilt will share in the cost of the stabilizer.