There is no clear explanation regarding this, but I am guessing three possiblities:
- The game ends and rewinds the time
- The game waits until a new players joins and finishes the game
- The game never ends, if only 4 players can play the game and new players can't replace the old dead players
The dead can't play the game and Jumanji wants desperately to be played. So most probably points 1 and 2 will be the consequences. After all in the first part Alan survived the jungle without survival instincts and the guy who was hunting him somehow never hit him.