On most airplanes, the stabilizer holds the tail down, not up. If the tail feathers were to fall off your typical sport plane, trainer, or scale model in flight, the nose would drop and the plane would start to do an outside loop.
This depends on the airfoil used and the balance of the airplane. But is generally correct. Most lifting airfoils used on aircraft have a negative pitching moment which means the airfoil wants to rotate nose down when creating lift. So in conventional designs without electronic stability systems the tail plane is pulling down when the aircraft is in normal 1g un-accelerated flight.