At an undetermined point in time, the bracket that supported the fuel flow transducer for the airplane's fuel monitoring system failed. This allowed the transducer to vibrate, and ultimately lead to the loosening of the B-nut on the fuel line leading to the transducer. Because the B-nut became almost completely disconnected from the transducer, approximately 40 gallons of fuel was lost overboard during the flight. Because the leak was upstream of the transducer, the fuel management system did not detect or display the loss of fuel, and the engine ultimately lost power due to fuel exhaustion. The pilot executed a forced landing at a non-controlled airport, and intentionally exited the side of the runway surface when it appeared that the airplane could not stop prior to departing the end of the runway and encountering a steep drop-off. After the airplane exited the side of the runway, it entered rough terrain and experienced a collapse of the left main landing gear. The collapse of the gear resulted in substantial damage to both the left wing and the aft fuselage.