[thdrdt]

I believe they use devices that act like some kind of radar. They send a signal across the wire and measure how long it takes to bounce back. They can get a really good estimation of the distance between the ping and the cut.

But maybe others can explain how this works.

Edit: this website explains other methods very well https://www.electricaltechnology.org/2015/06/cable-faults-ho...

[Koffiepoeder]

Also, fiber optics needs repeaters, so as a first rough estimate resource you can very quickly determine between which two repeaters the cable was broken.

[daemoncoder]

Time-domain reflectometry