The more conventional way is to put the noise into the cable from one end and listen with a receiver as you walk along the cable. The cable will probably emit less noise where it is balanced (before the break) and more noise after the break where only one conductor has survived.
A TDR can be fun to use, but electricity doesn't travel in cables at the speed of light. It can be as slow as 75%, depending on the dielectric.
Another way to find a break in cable is to use a variable frequency oscillator and find the resonant frequency of the stub. You still have to deal with the velocity factor. Yet another way is to build a simple one-transistor oscillator, using the stub as the principal resonator. Then measure its oscillating frequency.
Edit: Simple TDR shown above is the best idea. I'm going to build one for myself in case I ever need it!