How do we know that Abner Snopes doesn't die at the end of "Barn Burning"?

The easiest explanation for your question is that Ab Snopes appears in Faulkner's fiction after this run-in with Major de Spain occurs.  The Snopes family appears in numerous Faulkner's novels; Ab in particular plays a large part in The Unvanquished, and the family in general is anthologized in a trilogy which includes The Hamlet, The Town, and The Mansion, so named because they chronicle the rise of Flem Snopes, Ab's son, from a sharecropper to an influential man in Yoknapatawpha County.  The reader is led to believe that Major de Spain has shot Ab toward the end of the story when Sarty hears three shots fired, but he never goes to see what has happened.  Sarty both literally and figuratively turns his back on his father that night.  When read in isolation, the uncertainty of Ab's fate in "Barn Burning" is hardly imperative to understanding the story's basic themes of defining choice, honor, and integrity in a young boy's life.