With a little further thought, I guess that the pump and motor could also be bad, but wouldn't be the sole cause of this problem. To properly bleed the rear brakes, the pump and motor need to be running. If they were not running, no fluid would be pushed into the rear lines. So if someone opened the rear bleeders in that state, all the fluid in the lines would run out, but no replacement fluid would be pushed in. If the rear lines are empty, that could possibly factor in to your problem.
It would be helpful to know if the pump and motor run when you turn the key on. And if you open a rear bleeder, can you tell if there is fluid in the rear lines?