C172 instructor with student reported the engine completely shut down after practicing power-off stalls resulting in an off-airport landing.

Narrative

At approximately XA50 hr local; I was conducting flight instruction with Person A in a C-172G. During this time; we were conducting pre-solo maneuvers. At the time of the incident; we were already flying for .8 hours. During the event; we were conducting a power-off stall; at which point Person A conducted the maneuver and when he attempted to recover the engine failed to provide power and shut off. I immediately took over the controls of the airplane; performed the emergency procedure checklist items; and attempted to restart the engine. I attempted to restart the engine two times; where I ran the starter for approximately 5-9 seconds (can't remember the exact time). After I immediately turned the airplane towards an open field; which was open and away from any houses. I then [requested priority handling]; I attempted to contact approach control but did not get any response; so I passed all of the pertinent information to the blind. I received a response from an air carrier flight; in which I requested them to pass the information to ATC. Additionally; received a few other calls from other pilots in the area. I then continued to fly the airplane and was able to land the airplane on the open field without any injuries or damage to the airplane. After landing I informed on XYX.Z that we were on the ground safely; and again I asked to relay the information to ZZZ ATC.Prior takeoff: This was the third flight of the day on this airplane and the second lesson flight with Person A. We planned for two sorties on this day to catch up and the plan was to evaluate him to endorse him for his first solo flight. On the two initial flights and on the initial phase of the flight; the airplane performed flawlessly; with no issues with any performance; all ground checks were in accordance with the airplane checklist and check out. During the initial climb engine was providing normal power; 2350 +/- and a 500fpm climb; so performing within parameters. At this time the ASOS was reporting a Density Altitude of 2;900. We added 10 gallons of fuel which brought the total fuel on board to 20 gallons. The engine had 7 quarts of oil.During the flight: During the training flight; the airplane was performing as normal; we conducted all of the pre-solo maneuvers; we did steep turns; slow flight; power-off stalls; power on stalls; we had practiced an emergency procedure; S-turns across the road- and turns around a point. We practiced all these maneuvers IAW ACS standards. When the incident happened; we were executing the same maneuvers for a second time. There were no indications of any engine or systems malfunctions or issues. The engine did not show any signs of problems; I did not hear or notice any sputtering or loss of power until the recovery sequence when power was added; and no engine power came in and we had the total loss. The propeller stopped windmilling and the only time it moves was when I attempted to start the engine with the starter. After safely landing at the open field: Upon landing; and we did check each other and shook it off. I immediately called the owner of the airplane and maintainer and informed him of what happened; he immediately started driving to our location. The owner arrived; and I provided him with detailed information about what happened. We both checked fuel tanks and there were 15 gallons remaining of fuel between both tanks; we checked the oil and still had 7 quarts of oil remaining. He then proceeded to attempt to start the engine; the engine started after a few attempts. The owner started the airplane and was able to fly the airplane back to its home station at ZZZ1.