Emergency brake cables on many rear drum equipped vehicles are held in with a small metal collar that has little springy fingers. A fantastic design for the assembly line since all you do is insert the cable through the hole in the backing plate until the fingers spring out. If you need to remove the cable for replacement, it can be a real pain to get all the locking fingers to cooperate. As you push fingers down and make your way around the collar, sometimes the fingers that you previously pushed down jump out of the hole and lock back in place. It's just one of those situations where you need a third hand.
Try this little trick next time. Get a worm gear clamp that's slightly larger than the brake cable lock. Slide the clamp over the lock, but leave a small gap between the clamp and the backing plate. Tighten the worm gear clamp to squeeze all the little locking fingers down enough to slide the tips of the fingers through the hole in the backing plate. Once you get that far you can loosen the hose clamp and finish removing the cable.