On August 17, 2004, at 1350 eastern daylight time, a Piper PA-28R-180, N4631J, was substantially damaged during a hard landing and gear collapse at the Littlebrook Airport (3B4), Elliot, Maine. The certificated private pilot and certificated flight instructor were not injured. Visual meteorological conditions prevailed for the instructional flight that originated at the Sanford Airport (SFM), about 1330. No flight plan was filed for the flight conducted under 14 CFR Part 91. The pilot and the flight instructor provided telephone interviews. They said the purpose of the flight was to evaluate the private pilot for participation in the Federal Aviation Administration (FAA) Wings program. According to both individuals, the flight began at Sanford Airport (SFM), and the pilot was given a simulated engine failure in the traffic pattern. The subsequent landing attempt was aborted, and the flight was continued to Littlebrook Airport (3B4). Upon arrival at Littlebrook, a landing was performed to runway 12, and the airplane was back-taxied for takeoff and flight in the traffic pattern. The airplane took off, and while turning to the downwind leg, approximately 700 feet above ground level (agl), the pilot was given another simulated engine failure. During the descent, the airplane was configured for landing. The pilot turned the airplane to land on Runway 30. While turning to align with the runway, the airplane overshot the runway, and the turn was continued to the right to come back to the landing surface. About 6 feet above the runway, the airplane "stalled", "plummeted", and experienced a hard landing. The airplane shook during the landing roll, then veered right and departed the landing surface. The landing gear collapsed and the airplane came to rest. The instructor and the pilot then egressed the airplane. When asked if they experienced any problems with the performance or handling of the airplane, each said no. The weather reported at the Sanford Airport, at 1355, was scattered clouds at 4,000 feet with 10 miles visibility. The wind was from 200 degrees at 4 knots. The temperature was 73 degrees Fahrenheit, the dew point 57 degrees Fahrenheit, and the barometric pressure was 30.08 inches of mercury.