In "The Most Dangerous Game," what happens to the men if they choose not to be hunted?

In the short story “The Most Dangerous Game” by Richard Connell, people who refuse to be hunted are beaten to death by Ivan, a giant of a man who used to whip people to death for the Czar of Russia.

In this story, the villain is a man named General Zaroff.  Zaroff lives on “Ship Trap Island,” which is somewhere in the Caribbean Sea. Zaroff’s life passion is hunting. During his career as a hunter, he eventually became bored because hunting wild animals is too easy. He decided he wanted to hunt human beings since they are intelligent and would be more challenging to hunt. Humans are “the most dangerous game” to which the story’s title refers. Zaroff obtained Ship Trap Island and uses shipwrecked sailors (including some whose ships were wrecked thanks to false navigational lights that Zaroff rigged up at sea) as his prey.

When Zaroff tells Rainsford this, Rainsford wonders how he gets the men to agree to be hunted. Zaroff tells Rainsford that the men have the choice of possible death in the hunt or certain death at the hands of Ivan. When Rainsford asks, “Suppose he refuses to be hunted,” Zaroff replies,

"I give him his option, of course. He need not play that game if he doesn't wish to. If he does not wish to hunt, I turn him over to Ivan. Ivan once had the honor of serving as official knouter to the Great White Czar, and he has his own ideas of sport. Invariably, Mr. Rainsford, invariably they choose the hunt."

As you can see in this link, the knout was a brutal whip used in Russia to flog criminals. Very often, the criminal was beaten to death. Ivan performed this duty for the Czar and, Zaroff implies, enjoys inflicting pain on people.

The answer to your question, then, is that people who refuse to be hunted are handed over to Ivan to be beaten to death.