If it were me, I would be tempted to just hand blind-stitch the wayward fabrics in place, then finish quilting. You might also be able to hand applique a new piece if the seams have pulled too much, just use tiny stitches. The very first quilt I sold was a roman stripe of 5 colors and black triangles. I thought I had purchased new fabric, but in certain places it started to disintegrate. Since it had already been machine quilted, I hand appliqued a black triangle onto the "holy" places, then re-quilted the triangles. I was beyond embarrassed, but the client was very understanding and happy with my repairs. Thankfully.