At approximately 21:30 Pacific time, a Piper PA-28R-200 on short final for runway 16 encountered rotor wash from a helicopter operating near runway 16 at Pierce County Airport/Thun Field. No one was injured. The airplane experienced a roll, yaw, and sink rate excursion upon encountering the rotor wash. The crew applied corrective flight control inputs in an attempt to counter this excursion, but the airplane touched down in grass adjacent to the paved runway surface. The flight crew, which included a flight instructor and a private pilot receiving flight instruction for his FAA commercial pilot practical test, continued the landing rollout in the grass, but the airplanes nose gear collapsed.