While maneuvering during the instructional flight the flight instructor noticed that the engine oil pressure was “remarkably low”, and the engine oil temperature was “a bit high.” He took control of the airplane and flew toward nearby roadways in anticipation of a forced landing. The engine then began to run rough, vibrate, and lost partial power. Shortly thereafter, the engine vibrated “incredibly” and lost all power. The flight instructor was unable to restart the engine and performed a forced landing into vegetation. During landing, the airplane flipped over and sustained substantial damage to the wings and forward lower fuselage. Examination of the engine revealed that the Nos. 1 and 3 cylinder connecting rods were fractured near their crankshaft end. The remnants and fracture surfaces of the rods, as well as their respective journals on the crankshaft were discolored (blackened and bluish surfaces) and smeared, consistent with thermal stress/damage. The No.4 cylinder connecting rod remained attached to the crankshaft but would not rotate. The crankshaft end of the rod was discolored (black and rust colored), consistent with thermal stress. Bearing material was extruded between the rod and the crankshaft lobe. Holes were found in the crankcase near the base of the No.4 cylinder and on the bottom of each crankcase half. The damage and discoloration of the connecting rod and crankshaft components, as well as the reported loss of oil pressure, suggest a lack of engine lubrication. At the accident site, oil was found coating the bottom side of the fuselage, consistent with venting oil overboard during flight. However, it could not be determined if the oil exited through the breaches in the engine crankcase after the connecting rod failures, or, prior to the failures through some other path. There were no obstructions found in any the visible oil passages in the crankshaft, and the engine oil pump was undamaged, contained no debris, and operated smoothly. It is possible that one or more of the connecting rod bearings spun inside its race, blocking the oil passage(s), which would have resulted in thermal damage to the rods and crankshaft. However, given the evidence available during the engine examination, the reason for the lack of lubrication could not be determined.