I've often wondered if most passenger airliners have a CG envelope which would allow the CG of the airplane to be pushed outside the limits if enough passengers relocated to the front or back of the airplane.
If they do passengers might be surprised to know that if for some reason a lot of people got up and crammed into the back of the plane it might become uncontrollable.
If this is the case, the mental exercise could help illustrate how important an understanding of weight and balance is. It also highlights the importance of flight attendants as part of the air crew in their need to ultimately exert control over the crowd of passengers if the situation warrants it.
As a bit of background, I once wondered if Flight 93 during the September 11th attacks might have become uncontrollable because the CG shifted when passengers moved around the airplane. Although I once speculated that this could be the case, I am no longer speculating on the subject. I just want to mention that this is the scenario which made me wonder about the answer to the actual question. Since writing the original version of the question I learned about the CVR from Flight 93 and that it was intentionally flown into terrain by the hijackers.