The thicker shelf liner or rug stay works great! It's the one with the small puffy squares. I use it under my scooting serger pedal--no more movement. Now and then it needs to be washed off to remove collected lint, bits of thread and dust, and it will work like new again. This is on a hard floor. I haven't tried it on carpet.
I would think fabric sewed around the edges would reduce friction and not work as well. You really want the rubber to the floor! Lol