What is the horizontal stabilizer failure procedure?
This would fall under catastrophic failure and theres not much that can be done. You may as well ask what will happen if a wing falls off.

but..

UA232 Sioux City. The #2 engine (in tail) blew up and took out the hydraulic lines rendering all tail control surfaces (horizontal and vertical) inoperative. The crew found they could regain limited control of the attitude of the aircraft by varying the thrust on the wing engines, increasing thrust gave some pitch up, decreasing thrust-pitch down. This was due to the line-of-thrust being below the wing. The crew did a great job of getting the airplane back to the airport and heading down the runway. Even though it cartwheeled and burned, a lot of passengers survived, thanks to the crew's action.