While descending near the destination, the left engine stopped running. The pilot attempted 2 airstarts which were unsuccessful. He feathered and secured the left engine and requested radar vectors to the nearest airport. A visual approach was made to the Hunt Airport at Portland, TX. The pilot stated that he was having no difficulty in maintaining airspeed even with the gear down until he was on final approach. On short final, he extended full flaps. He stated that as soon as he put the flap handle down, he realized he made a mistake, but it was too late to take any action to prevent the aircraft from landing short. The aircraft touched down on rising terrain between the end of the runway and a nearby shoreline, traveled up the embankment and onto the runway, then burned. The pilot escaped with only minor injuries. The fire damaged left engine was disassembled, but no preimpact failure was found. Reportedly, the plane had not been flown since Feb 82. Before takeoff, the battery was dead.