While it is the case, by design and typically by regulation, that brakes have more braking force on paper than the engine and drivetrain can produce, in the real world it is not so straightforward.
ICE engines have active heat rejection and conventional brakes don't. So ultimately in any prolonged fight between an engine and brakes the engine will win.
Hot brakes have a lower coefficient of friction. This is the brake "fade" experienced on long downhill runs or heavy use, such as while towing heavy loads. In extreme cases brake pad outgassing, brake pad glazing and boiling brake fluid, all a consequence of heat, will degrade brake power.
Traditionally vacuum assist is used to amplify brake force in passenger cars. The vacuum reserve is, however, finite and little vacuum is available from an engine with a stuck open throttle. When the throttle is even partially open and the engine RPM is kept low (such as when fighting it with the brakes) the vacuum drops severely. When boost runs out brake force is greatly reduced. This all changes in heavier vehicles where more robust systems are employed, such as compressed air brakes with large pressure reserves.
Some vehicles have enough power to overcome the brakes on driven wheels. Some vehicles have "low range" gearing that can also easily overcome the brakes.
The situation described by helsinkiandrew was probably a combination of brake fade that emerged while fighting the engine and lack of brake boost due to low vacuum because the throttle was somehow stuck. But there isn't enough information to say for certain.
ICE engines have active heat rejection and conventional brakes don't. So ultimately in any prolonged fight between an engine and brakes the engine will win.
Hot brakes have a lower coefficient of friction. This is the brake "fade" experienced on long downhill runs or heavy use, such as while towing heavy loads. In extreme cases brake pad outgassing, brake pad glazing and boiling brake fluid, all a consequence of heat, will degrade brake power.
Traditionally vacuum assist is used to amplify brake force in passenger cars. The vacuum reserve is, however, finite and little vacuum is available from an engine with a stuck open throttle. When the throttle is even partially open and the engine RPM is kept low (such as when fighting it with the brakes) the vacuum drops severely. When boost runs out brake force is greatly reduced. This all changes in heavier vehicles where more robust systems are employed, such as compressed air brakes with large pressure reserves.
Some vehicles have enough power to overcome the brakes on driven wheels. Some vehicles have "low range" gearing that can also easily overcome the brakes.
The situation described by helsinkiandrew was probably a combination of brake fade that emerged while fighting the engine and lack of brake boost due to low vacuum because the throttle was somehow stuck. But there isn't enough information to say for certain.