I agree with Peckish completely. It is obvious that the quilt has not been well cared for for some period of time. You could spend all that time and supplies on trying to restore it (not repair) and it will still be an old quilt. It will not look good. The person who owns this quilt probably thinks it will look new and fresh again. I think I would tell her that it will still be an old, deterioriating quilt and that maybe a replica would be a better choice.
Some things just can't be restored.