Brakes Are Broke(n) AKA Austin-Healey Brake Line Arteriosclerosis

An Austin-Healey 3000 came into the shop with rear drum-brakes that would apply but not release. Dean removed the flex hoses that run from the hard brake line to the brake cylinders, cut one open to see what was inside, and found this:

Old flex hose nearly closed up with solidified (stuff?).

Old flex hose nearly closed up with solidified (stuff?).

Whatever was in the flex hose that used to be liquid was no longer liquid, and the resulting pinhole was so small that fluid could not exit the wheel cylinders once the pedal was released. The brakes were able to activate only because the pressure from the pedal application was so great that it managed to push fluid through the degraded line.