Okay, here's an example that will definitely result in a lawsuit. My stock (or any other instrument like futures, forex, etc) tanked and my account accordingly went down to $0. At this point, my broker MUST liquidate all my position. If the broker, however, did not sell my position and my account dips into the negative (say, $10,000) AND THEY DEMAND I ADD MORE FUND to bring my account back up to $0, then you can bet I will sue their ass. And I will win.
It you were trading futures/options you would not win. It is called going into debit and you sign a piece of paper acknowledging the risk. Broker than can come after your personal assets to cover deficit.