The pilot reported that while landing on a grass portion of runway 15, the wind shifted from a crosswind to a tailwind. During the landing roll, he was unable to stop before the end of the 2,430-foot-long runway. The airplane continued beyond the end of the runway and impacted a fence, which resulted in structure damage to the left horizontal stabilizer, left elevator, and left wing. The pilot stated that at the time of the accident, the wind was variable from 240 degrees at 25 knots gusting to 38 knots. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.