There is some non-stick stuff that you put under rugs. But I've had trouble getting it to stay in place. You could sew it on and then it would stay.
I was thinking of something else, though. An aunt (now deceased) gave us some t-shirt decorations made of needle-punch (like a rug, made with yarn). She sprayed or spread a product on the back that allows it to stick on the t-shirts, then taken off and stick on something else. It won't stick any more if it gets dirty. I think it was a product made by Alene. I looked for it in stores and I was never able to find it. Maybe someone else knows what it is.