I betcha it's the plastic coating over the spiral wire that is getting the cable casing stuck. It must have split and bundled up like a sock at one end jamming the casing in place. That will be a hard thing to fix as everything you need to get at is inside the TT. All I can think of is using as much pullingforce as you can on the spiral wire without damaging the TT and the holes where the cable comes out if. Porblem might be is if you do pull it out, some junk might get left behind in the TT if there is no continuous tube in there to gude the cable casing.
Internally routed brake cables were sort of the rage back in the mid 80's but it seems like it wasn't always such a good idea as what happened on your bike. That's why it's always good to check on the condition of the internally routed cables everytime you consder buying a used bike.

Chombi