Do you have a choice?? I can close my door upstairs, but as soon as I open it someone runs in. They have various spots they love- not all of them on fabric. But they love this room because of the sun and I have a really hard time denying them. I do try and put a sheet over my WIP if out on the cutting table. then if they lay on that, they don't hurt anything.
Oh...did I mention my pets are Siamese cats who know they rule the world!