exactly as Seawolf says...invol deny boarding.

Usually before it gets to that there are people who can be convinced (aka paid via miles, upgrades, cash or a combination of the three) to take the next flight. A route like LAX where there are 2-3 flights per day almost certainly would find someone willing to take a deal.

However, if not then they follow the rules to a T. I can't remember what CX's check-in time limit is, but the people who show up at the airport passed that time are probably going to be put on the next flight screaming and kicking (whereas normally, they'd try hard to get you on the original flight). And at worst, if nobody takes a deal and everyone shows up on time, they're going to tell (x) amount of non-MPC and non-status pax that they're SOL, and on the next flight.