See, scraps between 1/2 yard down to about 2" cut offs go to the critters. They love them. My mice girls KNOW when their little bin gets full, and they start bouncing around as I pick it up to give them. If it's large enough to sew, it makes hammocks, but the little bits - and SELVAGE! - get to their bins. This morning, I peeked at the girls, and they had strung the long trimmings all over and were snuggled in their minky mix hammock with piles of trimmed bits. Looked nice and toasty warm.
Everything else, or anything ravel prone or stringy just gets tossed. That's just too small to save in my world. And who wants fabric that falls apart when you look at it cross eyed? It'd just fall apart in shipping or waiting to fill a box. I do save a few trash bags of it to use for dog pillow stuffing, but I don't need that much. Shelter here doesn't take pillows, but they do like the fleece blankets.