Ford parking brake cables have been well-known for sticking since the mid '70s. Lubricating them is never the answer. The only fix is to replace them. If you cut the main cable going to the two rear cables, that won't address the problem. It's the rear ones that stick inside the casings. When this is a recent problem, as in when someone applies the brake for the first time in a long time, you can usually see a shiny spot about an inch long on the cable right where it comes out of the front of the casing. On a lot of Ford trucks and vans the right cable comes out of the rear of the backing plate and goes all the way around past the bumper. That really aggravates an already common problem.

If it is indeed a rear cable that's stuck, you can often get it to retract by flexing the outer casing. If it's not rusted solid, brake shoe return spring pressure will gradually walk the cable back to the retracted position.

Besides dragging brake shoes, a cable stuck in the partially-applied position will cause easy rear wheel lockup during normal braking. It can also cause chattering shoes and a failure of them to self-adjust over time.