Earlier quoted context omitted.
Many years ago, I was driving down the highway on my way to work and, when I pressed the breaks to slow down, the pedal just... went straight to the floor. I had to use the emergency break to slow down, get off the highway, and pull over. Luckily that still worked (I've owned many a car where that was the first thing to go). So, it turns out the breaks rotted off and fell off the car on the way to work. I had had it…
Wow you were lucky. There was a driver in the UK whose accelerator got stuck, then his brakes burnt out and he was on a notoriously busy road traveling at 135mph - he survived! See https://www.the-independent.com/news/uk/this-britain/help-i-...
The brakes of a car in good working order should be able to overcome the engine and stop the car even if the engine is stuck at full power. But you have to do it decisively. Push the brake pedal to the floor and keep it there until you've stopped. What often happens is people are (very naturally) confused and not sure what to do, they'll brake but not hard enough, stop braking when it doesn't seem to work, try again, etc. This can heat up the brakes to the point where they're no longer effective enough to stop the car, and then you're really in for it.