How do people have so little clue as to how their car works?
Power brakes, on a gasoline powered car, are run by intake manifold vacuum. It does not take a belt to run them. The entire accessory drive system could explode, and as long as the engine was still running, the power brakes would be completely unaffected.
Having said that, there is a significant vacuum reservoir, with a check valve preventing leakage, even when the engine is shut off.
Park your car on a hill. Apply the parking brake, and shut off the engine.
Leave it overnight. The next morning, don't start the car. Turn the key enough to unlock the steering column, but no further. Don't touch the brake pedal yet. Make sure it's in neutral, and release the parking brake. Once the car has started rolling, press the brakes, and see how easy it is to stop the car. Then, release the brake pedal, roll downhill, and press the brake to stop again. Still feels normal, doesn't it? And this is after the car has sat for several hours, rather than only seconds after the engine has stalled.
Now the third time, all bets are off. The vacuum reservoir on most cars has enough capacity for two full brake presses; some even more. Barring a vacuum leak, though, there will *always* be enough power assist to bring the car to a stop with power-assisted brakes.
This doesn't apply to diesels, which have no intake manifold vacuum, so usually run the power brakes with a belt-driven pump.