2x2 plate with round section and rubber bristles? Very strange piece with soft rubber bristles. Bought in a misc box from a garage sale for my son and daughter.
So, the curiosity bug bit me again.  The mysterious part appears to be a Kre-O "Motion Brick" which appeared in various sets. In my research I found that there is a variation (hollow vs. solid) in the studs, as shown in the picture.