I'm from CA and always have heard them called "dresser Scarves"....My Grandmother made a lot so we always covered whatever with one of them. I used to turn a lot of them into pillow covers, then I put them on the bed to show the work off. I have no idea what one would do with them today. But if it's for you as a memory, I would get creative and if it is thin, yes, I would back it with some muslin...good quality.......