Tina, this was one of my thoughts as well. I have used silicone caulk for a lot of things that I wanted non-slip (e.g., dots under lamp bases) or to protect from heat (missing handle cover on hot iron). I don't know how caulk would work on fiber, but it should stick as well to that as well as it does to anything else (although it might not stick to wool,but should stick to cotton). You could get really creative with it too -- dots, swirls, strips, squiggles, etc. Let us know if you try this.
The other thing you might try is tacking on silicone rings -- actually I think I remember my grandmother doing that with rubber canning rings.