The sport pilot was on a personal local flight that included a stop at a neighboring airport for fuel. During a 2 mile straight-in final to the neighboring airport, about 1 mile from the runway, the engine lost power. During the subsequent emergency descent and landing, the airplane struck a fence, and the fuselage sustained substantial damage. Following a postaccident examination by the pilot/owner, he reported that the fuel totalizer calibration was inaccurate, and that an empty tank was indicating 3.6 gallons of fuel available. The pilot reported no preimpact mechanical malfunctions or failures with the engine that would have precluded normal operation.