On October 5, 2024, about 1450 eastern daylight time, a Piper PA-28-161, N207AB, was substantially damaged when it was involved in an accident near Merritt Island, Florida. The pilot and pilot-rated passenger were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 personal flight. According to the pilot, the purpose of the flight was to build flight time with his safety pilot. During the initial climb after takeoff on runway 11, at an altitude about 200 ft above ground level, the engine started to run rough. The pilot then leveled the airplane, engaged the starter, and the engine restarted. He decided to return to the airport and, during the turn back to the runway, the engine lost all power, so they decided to land downwind on runway 29. They approached the runway at an airspeed of about 95 knots, which the pilot reported was fast. The airplane touched down near the end of the 3,601-ft-long runway. He noticed they did not have enough runway to stop, and both the pilot and passenger applied heavy braking. The airplane started to skid off the right side of the runway and impacted uneven terrain, during which the nose landing gear separated, resulting in substantial damage to the engine mounts. Federal Aviation Administration inspectors examined the airplane after the accident. The inspectors examined the engine’s oil filter and found no metal particulates. The inspectors noted that when the right fuel tank was selected, fuel flowed normally to the carburetor. When the left fuel tank was selected, no fuel would flow. Further examination of the fuel filter, carburetor screen, and left wing fuel tank screen revealed all were absent of debris contamination. The inspectors drained the left wing fuel tank and utilized a borescope to examine the interior for contamination, with none noted. The inspectors examined the fuel selector valve and found that the handle/fuel tank position indicator could be manipulated past the detent, and that the valve was worn. No evidence of any preimpact mechanical malfunctions or failures of the airframe or engine were identified that would have precluded normal operation. The operator did not notify the NTSB that the accident had occurred until 1 month after the accident. By that time, the airplane had already been examined and released by an FAA inspector and the operator without NTSB involvement. The airplane had completed seven 100-hour inspections before the accident. The airframe manufacturer’s service bulletin for the fuel selector was not applicable to this airplane due to the newer age of the airplane and newer design of the fuel selector.