Those bits would have to be damn small to make it up the shaft of the pin. Hard enough getting oil through those pins, much less pieces of the stopper.
I'm kind of surprised that a 21G pin did that to your stopper. Is the stopper well used, or do you poke the stopper at the same place sometimes? I wonder if it is just a cheap stopper or what. I draw with 20G, although I wish I had purchasesd 21G.