A: The Keepers offered up for combat have to already be in play in front of you. If there are not enough combatants (only one person has a Keeper in play) that entity simply wins by default. They stick their head in the Arena, see that there’s nobody there trying to kill them, breathe a sigh of relief, and get the heck out of there.
When in doubt, the general rule with things applying to Keepers is that the Keeper has to be in play in order to be able to “do things”. Usually that means using special powers, but in this case, it also means being obligated to fight in the Arena.