I recently built up a 90's Italian steel frame with internal brake cable routing. It's one of those where the cable and the housing both run through the top tube. Both had been pulled out when i got it.

I took the brake cable and put it in the front opening. In the back end, I put a loop of spare cable. I pushed the first cable till it went through the loop, then I pulled the loop out the hole, bringing with it the other cable.

Sounds easy, but it took a dozen tries.

Next, I fed the new cable housing over the brake cable. It went right through, no muss, no fuss.

So, I guess what I'm saying is, if yours is like mine, DON'T pull both the cable and the housing out!

I'd suggest feeding the new cable (with the original soldered end) through the old housing, then pull the old housing out and feed the new housing over the new cable. Voila! New cable and housing.