On September 19, 2018, about 1000 mountain daylight time, a Piper PA28 180 airplane, N8003W, impacted fencing and terrain during a forced landing near Pagosa Springs, Colorado, following an inflight loss of engine power. The airline transport pilot rated flight instructor and the student pilot were uninjured. The airplane sustained substantial damage during the impact with fencing. The airplane was registered to and operated by San Juan Flyers Inc. as a Title 14 Code of Federal Regulations Part 91 instructional flight. Day visual meteorological conditions prevailed in the area about the time of the accident, and the flight was not operated on a flight plan. The local flight originated from the Stevens Field Airport, near Pagosa Springs, Colorado, about 0900.According to the flight instructor's accident report, the flight instructor was introducing engine failure emergency procedures to the student pilot. Emergency procedures were reviewed inflight, the instructor located a landing spot, and pulled the throttle to idle to simulate a loss of engine power. The student pilot conducted the emergency procedures on the left side of the cockpit that included switching the fuel tank selector position from right to left, verifying the primer was in and locked, turning on the fuel pump, checking magneto operation, and turning the carburetor heat on. The flight instructor subsequently added power to go around about 600 ft above the ground. The engine sputtered. Emergency procedures were reviewed again and the flight instructor noticed that the fuel pressure indication was zero. The flight instructor did not check the fuel selector nor could the selector be seen due to its location. The flight instructor subsequently performed a forced landing during which the airplane impacted fencing and ditches before coming to rest in a field. Following the accident, the flight instructor observed the fuel selector valve was about 1.5 to 2 inches between the left detent and off positions. Subsequent to the accident, a Federal Aviation Administration inspector examined the accident airplane at the accident site. The airplane's engine was started, and the engine was operational. The flight instructor reported no preimpact mechanical malfunctions or failures with the airframe and engine that would have precluded normal operation and had a safety recommendation to double check the fuel selector valve position during the forced landing demonstration.