There are cables to the stabilizer and two electrical trims, one for manual and one for the autopilot (roughly from memory without looking in any books or checklists).
If the stabilizer is stuck, it's stuck and won't move. Therefore, most likely, the restriction on the flaps, since you will only have the elevator to counter the nose down.
The cable to the stab does not run away. Only a malfunction in one of the electrical trims will cause a runaway. The manual trim wheel can still move the stabilizer, once the electrical motors are cutout with the cutout switches, and hence compensate for flap selection.