I worried about my cats sleeping on my ufos, but my cats are so clean that the fabric is probably worse off for me touching it than it is for anything they might do. I didn't like my cat rubbing against my hand when I'm cutting though, so I made her a bed out of some old pillows and a scrap of fleece. She didn't like it at first, but then I got some dried catnip and sprinkled it over the fleece. Now she loves it and she stays off my projects. I call it "kitty cocaine."