It reached the bottom. Probably hit one of these: http://elevation.wikia.com/wiki/Buffers

Note that it wasn't descending particularly quickly; one cable snapped but other safety systems were still operable.

The best book ever for understanding how Elevators work is a wonderful late 20th century work of fiction called The Intuitionist by Colson Whitehead, which was described by its author as what you would expect to happen if you let a child grow up reading elevator manuals.

Entering “elevator safety mechanism” into google will bring up several links with explainations. The first link for me references this story.

There was an elevator hacking talk that went into the buffers at the bottom of the elevator. You may have seen them in elevators that have glass on the outside of the shaft like in malls and hotels. The elevator never rests on those. Those are to take the impact of an elevator that crashes. Inspectors will often test the buffers as well as part of routine maintenance:

https://www.youtube.com/watch?v=ZUvGfuLlZus

The basic theory is that between the car and the wire there is a spring connected to brakes. When the car hangs in the wire this spring is loaded and the brakes disengage, if the wire breaks, the spring returns and brakes engage. All this is mechanical.

What I never understood is how elevators can travel downwards so quickly without such a system engaging. Can they block it somehow or are they never accelerating fast enough down?

I’d also like to know what they meant by “plunges”. How fast did it descend? Was it in free fall?