On September 17, 2017, about 1347 Pacific daylight time, a Piper 28-161 airplane, N2587X, experienced a loss of engine power while on downwind for runway 27L at Gillespie Field Airport (SEE), El Cajon, California. The certified flight instructor (CFI) sustained minor injuries and pilot rated passenger was not injured. The airplane sustained substantial damage to the left wing. The airplane was registered to and operated by the pilot as a Title 14 Code of Federal Regulations Part 91 personal flight. Visual meteorological conditions prevailed, and no flight plan was filed. The flight originated from SEE at about 1250. The pilot reported that after flying around the area they returned to the airport to practice a few touch-and-go landings. The first two left traffic touch-and-goes were uneventful; after the third takeoff, the tower informed them to make right traffic. While on downwind they were cleared to land; the pilot reduced power and started to descend. After turning base, the pilot increased power, but the engine did not respond and remained at idle. There was no change in engine noise and the engine was not running rough. Both pilots manipulated the throttle several times, but the engine did not respond; they also manipulated the primer, but to no avail. The pilot elected to land the airplane onto a nearby road. During the descent the airplane struck powerlines and a tree, before it impacted the roadway and slid to a stop. A postaccident engine examination revealed no anomalies that would have precluded normal operations. The throttle and mixture controls moved freely from stop to stop. The gascolator bowl was removed and the screen was clear of debris. The oil filter was removed and opened; oil was present and no contaminates or debris were noted. The spark plugs were removed from the engine and exhibited wear consistent with normal operations per the Champion check-a-plug chart. The rocker covers were removed and the propeller was rotated by hand. Spark was obtained in proper firing order and the rockers moved at the appropriate time. Thumb compression was obtained on all cylinders, except for the number 2 cylinder. Further examination revealed the intake valve was unseated due to impact damage. The engine was boroscoped and all cylinders exhibited normal operating signatures. The carburetor bowl was removed from the engine. The fuel screen was clear of debris; the carburetor bowl was removed and no fuel was present in the bowl or the accelerator pump well. The floats were intact and undamaged. Air was blown from the gascolator to the wing root, as well as from the electric driven fuel pump to the carburetor inlet; all lines were clear of blockages and debris. At the time of the accident, weather at SEE reported a temperature of 25°C and a dewpoint of 15°C. A review of the carburetor icing probability chart, located in the Federal Aviation Administration's (FAA) Special Airworthiness Information Bulletin CE-09-35, dated June 30, 2009, revealed that the airplane was operating in an area favorable for the formation of serious carburetor icing at glide power. On scene photographs provided by the FAA inspector revealed the carburetor heat lever was in the off position.