Good chair mat works with worn carpet my carpet is almost to the bare floor and it sticks very well. I wish it could be a little larger by 2 inches all around but OK so far.
Nothing like trying to scoot around on your desk chair on carpet. NOT. Using the heavy plastic desk mat that anchors into your carpet without harming it saves the day. I can scoot from in front of my screen to the filing cabinet to the supply drawers with ease.