Yeah there's special tech for that! Has something to do with sending some frequency over the line and measuring how long it takes to "reflect" off of the breakage and back to the shore.
In the non-optical domain, that used to be a feature in the most expensive cable measuring gears (to the tune of €25k about 20 years ago).
I had the pleasure of using one of the devices that had that when I wired my old house. Borrowed the kit from ... an institution that allowed me to get their gear for a weekend. (Yes, I knew people in there.) Having the device tell me that a given strand in a CAT5e cable was faulty at <this many meters> from my location made it surprisingly easy to detect where I'd messed up.
I was going to say that this was invented by none other than Heaviside, but it turns out his technique relied on static resistance measurement to find the cable fault. Similar concept though. And in 1861!