"...short-stroke a pump gun <click>, but not jam it..."

What happens is that a round trys to feed from the mag, but gets jammed under the partially closed block. The fired round is usually ejected just prior. To clear the jam, you depress the action bar release with the strong hand, grasp the forearm with the the weak hand, and strike the butt against the ground (or any hard surface) HARD. That will eject the jammed round out the bottom, you then push the forearm forward and you are good to go. It can sometimes damage the follower, so don't try this at home (unless it is a real emergency)...