The pilot receiving instruction and flight instructor were conducting a 1,020 nautical mile (nm) cross-country flight, with multiple planned fuel stops. Upon arrival at one of their planned fuel stops, they discovered that no fuel was available at the airport. The pilots elected to proceed to another airport located about 53 nm away. While enroute at an altitude of about 6,500 ft, the left and right engines began sputtering. The flight instructor stated that they were running out of fuel, and shortly thereafter, both engines experienced a complete loss of engine power. Unable to maintain altitude, the pilots conducted an off-airport landing in an open field. During the landing roll, the right main landing gear collapsed, and the right wing impacted the surface, resulting in substantial damage to the right-wing spar. A post-accident inspection of the airplane revealed that the left-wing fuel tank was empty, while the right wing contained a small, undetermined amount of fuel. A Notice to Airmen (NOTAM) which advised fuel was not available at the airport was issued about 1 month prior to the accident and was still in effect at the time of the accident.