There was that time in the not that distant past when the gate agent's pass reader was this giant console that would slurp in your boarding card -- printed on real card stock with a magstripe on the back -- and would register your name, then eject that stub from a slot in the top for you to take on your way to the jetbridge door.
Not since those machines were retired (I haven't encountered one in five or six years) have I had any airline employee tear off the stub. Why can't they do away with that?