I know Captain Wings writeup is based on hang gliders, but the inclusion of the word aircraft came to my attention, and I would like to make a correction. Airplanes are a category of aircraft, so I will relate to them. Airplanes do not lose ALL response to aerodynamic control inputs. While the wing of an aircraft will lose lift during a stall, aerodynamic control inputs do not completely cease to respond. The ailerons will not be functional, as they rely on airflow over the wing, however, the elevator and rudder still work. Operation of the elevator is critical to the recovery of a stall. It is needed in order to decrease the angle of attack and resume smooth airflow over the wings, and as a result, the restoration of lift.
Rudder control is needed in case the stall develops into a spin, first the spin needs to be stopped by applying opposite rudder, then the stall can be broken by decreasing the angle of attack with forward control wheel pressure.