Hello everyone, I hope this is not the wrong place to ask. I’ve just changed my bike’s brakes (caliper type mechanism) because one of the two cable jackets did this (the black part correctly stops at the brake lever but the central part is smaller and is able to enter the brake lever). After changing to a new one at the front, I tensioned the back one and it broke the same way after a few tests. Am I doing everything wrong? (The bike is really old and rusty but seems to me I can only upload 1 pic per post)
Edit: link to some more photos


Thanks for the clear explanation, yes definitely broken then