On April 30, 2006, about 0840 mountain standard time, a Piper PA-44-180 (Seminole), N449PA, veered off the runway and collided with a sign at Deer Valley (KDVT), Arizona. DVG Holdings Incorporated, d.b.a. Pan Am International Flight Academy, was operating the airplane under the provisions of 14 CFR Part 91. The certified flight instructor (CFI) and the private pilot were not injured; the airplane sustained substantial damage. The local instructional flight departed about 0735. Visual meteorological conditions prevailed, and no flight plan had been filed. The CFI submitted a written report. He and the private pilot were inbound on an instrument approach to runway 7R while simulating a right engine failure. The CFI set the right-hand engine at 11 inches manifold pressure to simulate that the engine propeller was feathered. Before reaching the missed approach point, he instructed the student to continue the approach visually. About 20 feet from the touchdown point, he gave the student control of both throttles and pulled them both to idle. The sink rate was excessive, and they bounced into the air. The CFI told the student to execute a go-around procedure. Both throttles were set to full forward and the right engine never regained power. The airplane was below its minimum controllable airspeed, and it then yawed suddenly to the right. The CFI proceeded to take the controls from the student. He reduced the throttle on the left engine to regain control of the airplane. Their altitude was approximately 40 feet above the ground and they were descending rapidly. He called the tower to report their emergency landing on taxiway Charlie. He attempted to maintain a straight heading. They hit an airport sign, and the nose gear collapsed. The airplane skidded about 20 to 30 feet before stopping on the airport ramp. The Federal Aviation Administration (FAA) Principal Operations Inspector (POI) interviewed the CFI and student. The CFI stated that he did not recall turning the fuel selector to the off position, and did not think that his student did either. However, he did not recall verifying its position prior to landing. He does not shut the fuel off for single engine practice when low to the ground. The student did not recall turning the fuel selector valve off. A maintenance technician submitted a written report. She arrived at the scene of the accident and secured the airplane. Upon entering the cabin, she saw that the fuel selector for the right engine was in the off position, and the fuel selector for the left engine was in the on position. She notified her supervisor of this observation, made sure all switches were in the proper position, and then shut off the fuel selector. The POI oversaw the examination of the airplane. Maintenance technicians found no fuel in the right fuel line, carburetor, or fuel pump. They turned the fuel selector valve to the on position. One of them started the engine without difficulty, and they observed no anomalies while they ran the engine.