Are most of the blocks embroidered? If so I might be tempted the hand appliqué frames to the blocks to hide the frayed edges and preserve the whole quilt. If only a few blocks are worth saving then I would probably take the quilt apart, put stabilizer behind the blocks, re-sash, quilt and bind. HOWEVER if the quilt is historical than you would need to preserve it as is. A museum site would give you pointers on doing that.