Near the end of "The Most Dangerous Game," Rainsford has exhausted his defensive knowledge of hunting and is at his wit's end. He has lost his knife, killed only Ivan instead of Zaroff, and is "treed" against the cliffs of the island, where there is nothing but violent waves and sharp rocks.
"Nerve, nerve, nerve!" he panted, as he dashed along. A blue gap showed between the trees dead ahead. Ever nearer drew the hounds. Rainsford forced himself on toward that gap. He reached it. It was the shore of the sea. Across a cove he could see the gloomy gray stone of the chateau. Twenty feet below him the sea rumbled and hissed. Rainsford hesitated. He heard the hounds. Then he leaped far out into the sea....
This culminates all the suspense before, with Zaroff allowing Rainsford to escape to prolong the hunt and Rainsford slowly tiring himself out. Other prisoners have run to the shore but always turn to face the dogs; Rainsford, knowing that fighting the dogs and then Zaroff with his gun can have only one end, decides that he has nothing to lose and jumps. In this manner, he shows his willingness to live on his own terms stronger than his willingness to let himself be killed; even if he had drowned in the ocean, it would have stolen the kill from Zaroff, since that is all Zaroff cares about.
Rainsford's appearance at the end could be seen as a second, smaller climax, but it is deliberately understated to show how he has been affected by his ordeal, and so it acts more as an epilogue.
The climax of this story would be when General Zaroff brings Ivan and the whole dog hound to try to capture Rainsford, but Rainsford runs away, and jumps into the water, swimming back to the chateau for safety.