The really scary part was after dialing the number and encountering the operator, we were unable to hang up (any time we hung up and picked back up, the operator was still there, even after waiting about two minutes). Fortunately this was (a) at MIT which still had a central electromechanical telephone switch for student phone lines in the '80s and (b) I had keys to the switch as a student phone repair tech.
I still remember grabbing my keys, running over to the switch, and physically pulling the relay contacts to release the call and prevent a trace to our location in case that was the motivation for holding the line (nowadays traces are digital and instantaneous, but when looking at old-school electromechanical switches you really did need time to trace the call physically through the relays).
Yes, we were aware the operator was probably just messing with us by showing he could hold our line against our will to discourage us from calling again, but it still scared the crap out of us just in case.
We pulled out a paper phone book, devised a set of criteria for potentially interesting superficially invalid phone numbers, and started dialing them. On a rotary dial phone. And we found one pretty quickly. And it was a much scarier experience than we had expected.
The exact number we dialed is unfortunately(?) lost to the passage of time.
It's analogous to finding the hardware corresponding to someone's network address by being able to inspect the routing tables of all the intervening routers. Even if they turn their computer off, you can still trace them back to the physical line.