On September 14, 2017, about 1130 eastern daylight time, a Beech C23, N2120W, operated by Maine Instrument Flight, was substantially damaged during a forced landing, following a total loss of engine power while on approach to Machias Valley Airport (MVM), Machias, Maine. The private pilot was not injured. The instructional flight was conducted under the provisions of Title 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed and a visual flight rules flight plan was filed for the flight that departed Augusta State Airport (AUG), Augusta, Maine, about 1015.The pilot was accruing cross-country flight experience for his commercial license. The pilot reported that he and his flight instructor reviewed his flight planning for a three-leg cross-country flight and he departed with full fuel. During the first leg, about 10 miles from MVM, the pilot descended the airplane to the airport traffic pattern altitude. While in the traffic pattern, as the airplane was turning on to a left base leg for the runway, the engine began to run rough. The pilot verified that the mixture was full rich and the fuel boost pump was on. He also applied carburetor heat, but the engine lost all power about 15 to 20 seconds later. The pilot then turned the airplane directly toward the runway, which resulted in a 45°-angle to the runway threshold. The pilot realized that the airplane was not going to glide all the way to the runway threshold and prepared to land in a grass area just prior to the runway. During the landing, the landing gear sank into soft ground and the nosewheel touched down hard, which collapsed the nose gear. The airplane spun 180° and came to rest upright in the grass area. Examination of the airplane by a Federal Aviation Administration (FAA) inspector revealed damage to the right wing spar. The inspector noted that 20 gallons of fuel per wing were removed from the airplane. The magnetos, fuel boost pump and engine driven fuel pump tested satisfactorily. The carburetor was intact and its screens were absent of debris. The fuel bowl was also absent of debris. The inspector rotated the propeller by hand and noted camshaft, crankshaft, and valve train continuity to the rear accessory section of the engine. Due to damage to the engine mounts and exhaust system, an engine test-run was not attempted. The inspector added that the engine had accumulated about 359 hours since major overhaul. Hancock County-Bar Harbor Airport (BHB), Bar Harbor, Maine was located about 40 miles west of the accident site. The recorded weather at BHB, at 1156, was: wind from 180° at 5 knots; visibility 10 miles; sky clear; temperature 24° C; dew point 17° C; altimeter 29.83 inches of mercury. Review of an FAA Carburetor Icing Probability Chart for the given weather conditions revealed, "Serious icing (glide power)." Review of a descent checklist from a pilot operating handbook for the make and model airplane revealed, "2. Carburetor Heat - FULL ON or FULL OFF, AS REQUIRED."