On July 20, 1993, at 1800 eastern daylight time, a Piper PA28- 140, N5764W, collided with a fence while attempting a precautionary landing at a private airport near Poplar Branch, North Carolina. The personal flight operated under 14 CFR Part 91 with a valid visual flight plan filed. Visual weather conditions prevailed at the time of the accident. The airplane was substantially damaged, and the two occupants on board the airplane were not injured. The flight departed Statesboro, Georgia, at 1420 hours. According to the pilot, he had flown between Statesboro and Elizabeth City several times and always reached the destination airport with approximately one hour of fuel on board. During this flight, he encountered weather conditions which required him to deviate from his planned course. After the engine sputtered a few times, the pilot realized that he was near exhausting his fuel supply and began searching for a place to make a precautionary landing. After several minutes of searching, the pilot located Pine Island Club Airport. During the landing roll on the north runway, the pilot lost control of the airplane, veered off the runway and collided with a fence. The pilot also stated that, the engine continued to operate throughout the entire approach and landing procedures. There was no fuel in either fuel tank when the airplane was examined at the accident site.