^^^ what he said.....
If the inner cable has some corrosion then yep, you'll free it off with penetrating fluid and if you pull it off the car to give it a proper soaking you might even get it sliding again.
But it's never going to work properly in the long term. My experience has been that I can get old cables moving freely and yep, they will apply the brake. But there's a yard or more of outer casing on either side of these rear cables and when you have some dirt, rust, etc, inside, that's a lot of friction for a couple of return springs to overcome. So I've found they never release smoothly after a few days and gradually seize up again over time.
If it's truly stuck and the cable is showing signs of corrosion, flaking plastic covering, etc, then I'd use the Mk 1 angle grinder to remove and get a new one ordered up. Life will be so much easier....
Brian