Got a giggle from Rob's reply. The log cabin I think I would have had fun with. Sometimes those unsalvagable are interesting to someone else. Sometimes I think, "It can't get any worse", through rules out the window and have fun playing.
One time a quilt top was donated to "comfort quilts". It was truely a disaster. Looking back it reminded me of a lady with dimentia who kept knitting the same ball of yarn over and over. She just needed to keep her hands busy. It didn't matter the quality. Back to the donation, I took it apart. Tossed out the double knit poly, cordaroy, holy and worn out fabric. Ended up making 5 quilts of what was left (adding some of my own fabric). Since the goal was to use that fabric I got very creative and had fun with it.
Notice: some fabric made it into the trash.
I've also, slashed a project into unrecognizable pieces so wouldn't be tempted to try to salvage it from the trash.