Yes, no choice but to replace.
I noticed a while ago that the cable to my front derailleur was frayed a bit some time ago but was too lazy to sort it. The other day, pedalling to catch a main line train (fixed ticket) it bust as i was trying to get up to the big chainring. So i had to complete the journey in the bottom gear range with a fair amount of spinning out. Thank goodness for the 11 tooth sprocket on the back, and of course that it wasn't a brake cable.
Thanks for the post OP - i will check my brake cables in future - i have, very foolishly, tended not to.
You might also care to check the cyclist down thread for the story of the unfortunate rumanian woman. I don't know the exact cause but that was apparently a brake failure of some sort.