On August 20, 2018, about 1705 Hawaii standard time, a Piper PA-28-180, N98146, was substantially damaged when it was involved in an accident near Mokuleia, Hawaii. The flight instructor, student pilot, and passenger sustained minor injuries. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight instructor reported that, before the flight, he called the fixed base operator (FBO) and requested that the airplane be refueled "to the tabs." A preflight inspection revealed no anomalies, and the fuel was at the tab level as requested. They departed on the flight and conducted maneuvers at altitude before returning to the airport for touch-and-go takeoffs and landings. While taking off during the third touch-and-go, the engine lost power about 300 feet above ground level. The instructor took control of the airplane and initiated a forced landing to an open field south of the runway. During the landing, the airplane impacted a fence and came to rest upright. The student pilot reported that the flight instructor did the exterior preflight inspection of the airplane, and only recalled him looking in the right-wing fuel tank to verify the fuel level. Examination of the airplane by a Federal Aviation Administration inspector revealed that the right wing and fuselage sustained structural damage. The inspector reported that, during recovery of the wreckage, the left-wing fuel tank contained no fuel and was undamaged, and the right-wing fuel tank contained about 7 to 8 gallons of fuel, with a slow fuel leak. The fuel selector valve inside the airplane was set to the left-wing fuel tank, and all other engine controls were in the "off" position. The instructor reported to the inspector that, after the initial egress, he reentered the airplane and placed all controls in the off position and but did not touch the fuel selector. In order to facilitate an engine run, the starter was replaced, and one ignition lead was repaired. The engine ran uneventfully for an unspecified amount of time before it was shut down. The manager of the FBO reported that they received a request for fuel on the day of the accident for the accident airplane; however, they did not refuel the airplane. The FBO employee that was conducting aircraft refueling the day of the accident reported that he never received a call from his dispatch to refuel the accident airplane.