Cut the remnants into cotton yarn. Googling will give you lots of tutorials. I have been making potholders on the little child's loom since second grade and still like these woven ones best of all. Cotton loops have been getting hard to find and horribly expensive. I make loopers for the loom by cutting rings from orphan socks and tee shirt sleeves. I have also used the continuous tee shirt yarn on the loom instead of the loopers.
Many kinds of remnants can be made into rag rugs via crochet, needle weaving, hooking, sewing scraps to a solid backing or braiding. Works best to limit each project to one type of material. The web is full of up cycle tutes and ideas.