This is a difficult problem. If it is just that the stitching is coming out, you can re-sew them using a blind stitch. You could also use an overcast stitch, but your stitches would show a bit.
If it is that the fabric is tearing or fraying, it kind of depends on whether it is just one of the fabrics or both. If it is just one, you could blind stitch a replacement fabric on top of the one that is tearing or fraying. If it is both of the fabrics, and it is all over the quilt, it might be time to replace the quilt :-/
Happy Quilting!
Penny Halgren
www.How-to-Quilt.com
