I have never observed TeroTuf moving. I have used several sheets of it on rough use knives. Not really my favorite composite, but it is tough. I keep a sheet or two in the laminates box for use on camping type knives and tools that will get used and abused. It is merely polyester cloth (boatbuilding and auto body repair) and polyester resin. It is softer than the fiberglass/epoxy laminates (G-10) or the phenolic/cloth laminates (Micarta). Polishing TeroTuf to a shine can be tricky without the right abrasives and equipment (best done with diamond compound and polyester belt on a VS grinders or on a clean muslin buffing wheel). Otherwise, it gets a somewhat dull ( but grippy) finish. For my money, Micarta is far better on a knife.
Horse stall matting also makes a tough and light handle for non-pretty knives. The grip is probably the most secure, wet or dry, of any handle material.