One way that can happen to you is to be traveling the Canadian side of the Niagara River on your Sea-Doo jet ski, get caught in the rapids and swept over to the U.S. side. Jason Haist of Toronto was knocked unconscious and nearly drowned in the process, but his legal troubles were only beginning, as U.S. Border Patrol agents filed charges against him. They also arrested his cousin Edward, who tried to help him, for not reporting immediately on entry. After a press outcry, the two were released from their jail cell and returned to Canada. (Toronto Star, Aug. 25; Inside Toronto, Aug. 26).
P.S. Commenter “Buffalo” says the facts are more complicated than would appear from the Canadian press coverage and that “before the accident/injury, there was reportedly evidence that they landed on the US side without reporting in”.