Originally Posted by bearisgray
Without seeing this piece up close:
My guesses:
Loosely woven fabric
Fabric may not have been 100% cotton
Very narrow seams
Uneven shrinkage when washed
I agree with bearisgray. The only way I could think of saving the quilt is to machine quilt it. You could do a serpantine stitch along all of the seams. In case you are not familiar with a 'serpentine' stitch, it is like a zig zap stitch only the where the zig zag stitch is pointed, the serpentine is rounded. Most machines can do this stitch with the proper adjustment to the zig zag stitch.
By doing the above stitch, you can at least tack down all of the seams and keep any new seams from ripping out. Or you can free motion quilt all over the quilt to stablize all of the quilt. If you don't know how to free motion, this would be a good time to learn.
So sorry this happened to you. It sounds heartbreaking.