IN the actual ending of Richard Connell's "The Most Dangerous Game," Sanger Rainsford is successful at beating General Zaroff. Zaroff allows his "prey" three days to allude him. If his "prey" is successful, he states that the prey will be set free. To this point in Zaroff's games, he has never lost (up until his challenge with Rainsford).
Given that Rainsford is able to beat, and kill, Zaroff in the original text, an alternative ending would reverse who the victor is. Therefore, a possible alternative ending would have Zaroff finding success over Rainsford.
Another possible ending could extend Connell's ending. One could set Rainsford as the new hunter in Zaroff's game. In this ending, one could expand upon Rainsford's role as the new hunter, how his mindset has changed, and what his plans are for his "most dangerous game."