In William Faulkner's "Barn Burning," the resolution is open-ended: we don't know for sure.  But, I've always assumed that Abner died from being shot:

...he heard the shot and, an instant later, two shots...

First of all, barn burning was a capital offense in the South at this time.  De Spain would have anticipated Snopes would go after his barn or house, so he and his men would have been on stand-by, horse and gun ready.

So, these guys are ready to kill.  Sarty tells them what's up. There's no shooting in the air.  The first shot probably missed, because it's midnight.  The second two, in quick succession, would have been more accurate.

Three shots, I think, must have done the trick.  Abner doesn't seem like the quickest cat in the barn, so I think one one of these last two hit him.  And I don't see Abner running from a fight.  So, he stayed and faced his enemy.  Took one at close range.  Seeing as the man on the horse had a tactical advantage, Abner couldn't escape this barn burning.

Sarty does escape.  He runs, crests the hill, and in the darkness, keeps running.  The story ends with "He did not look back."