Just prior to the flight, the helicopter had been released by the maintenance section after troubleshooting a squawk concerning a "binding collective." The student and instructor (CFI) departed on a local flight and flew about an hour practicing precision hovering and rapid decelerations. During the rapid decelerations, the aircrew felt a binding condition in the collective and made a note to inform the maintenance section. After the last rapid deceleration, a climb was made to 1500 ft MSL. While rolling level from a turn at 45 to 50 mph, the aircraft shook violently, a loud "bank" was heard and the helicopter began a descent as if the collective had been slammed to the bottom. With the collective full up, engine and rotor RPM over the green arc, the helicopter descended as if it were in a full autorotation. Cyclic and antitorque pedals were used to avoid power lines, but the main rotor struck a tree and the helicopter crashed and burned. Only overload failure was found in the collective components.