On February 26, 1999, about 0945 Eastern Standard Time, a Cessna 172N, N737MJ, was substantially damaged when it overran the end of the runway at the Camden County Airport (19N), Berlin, New Jersey. The certified flight instructor (CFI) and student pilot were not injured. Visual meteorological conditions prevailed and no flight plan was filed for the instructional flight conducted under 14 CFR Part 91. The CFI stated they had departed the Trenton-Robbinsville Airport intending to land at 19N. Upon arriving at 19N, the UNICOM frequency advised that the winds were shifting and Runway 23 was the active. The CFI decided to perform a fly-by to visually look at the windsock, which confirmed the winds were favoring runway 23, although there would be a 60 degree crosswind. The CFI re-entered the pattern to land on runway 23. As the airplane crossed the threshold on final approach, at approximately 60 knots, with 20 degrees of flaps, the CFI retarded the throttle to idle. The CFI then observed the wind shift to a tailwind and the ground-speed of the airplane began to increase, causing the airplane to float. The airplane touched down with about 660 feet remaining of the 3,102 foot runway. The CFI applied maximum braking and retracted the flaps to decrease lift, and put more weight on the wheels. The airplane then ran off the end of the runway, hit a fence, crossed a road, and came to rest upright on a railroad single track. Examination of the wreckage by a Federal Aviation Administration Inspector, revealed that the flaps were only retracted to about 10 degrees of deflection. The flap selector switch, located in the cockpit of the airplane, was found in the 10 degree position. An airport, located 15 miles to the northwest, reported winds from 320 degrees at 17 knots, with peak winds to 27 knots. The pilot did not report any mechanical malfunctions with the airplane.