What happens if a creature that would fight isn't on the battlefield anymore?
It depends what the targets are.  The ability will resolve, but it may not do anything.

Scenario 1:


You activate Ulvenwald Tracker targeting your Grizzly Bears and your opponent's Runeclaw Bear
Your opponent responds with Lightning Bolt targeting your Tracker


In this case, the Tracker dies, but that doesn't affect anything.  The Tracker's ability resolves and the two Bears fight each other and both die.

Scenario 2:


You activate Ulvenwald Tracker targeting itself and your opponent's Suntail Hawk
Your opponent responds with Lightning Bolt targeting your Tracker


In this case, the Tracker's ability still resolves, but it doesn't do anything.  Spells and abilities don't track targets when they change zones.  That means that when the Tracker's ability resolves, the Tracker is no longer a legal target.  The ability still has at least one legal target (the Suntail Hawk), so it resolves.  It attempts to do as much as it can with the remaining targets, but the Hawk doesn't have anything to fight, so nothing happens.