Of the four authors named here, Fitzgerald and Hemingway are the ones specifically identified as exemplifying the "Lost Generation," as Gertrude Stein described them. In "Hills Like White Elephants" and in "Babylon Revisited" the theme is that of disillusionment, and of a past that can't be recaptured. Hemingway's story shows a couple for whom the magic they once had is gone. Fitzgerald shows the protagonist, a version of himself, going back to a kind of washed-out Paris during the Depression of the 1930s. The high-flying life he'd had during the Jazz Age in the 20s is over, and his focus now is on regaining custody of his daughter.
The stories by Faulkner and Wright would seem to have little in common with these Jazz Age tales. Both take place in rural America, as opposed to the European world of American expatriates so often depicted by Hemingway and Fitzgerald. Yet the thematic link might be that all four stories deal with lost innocence, or at least, with a lost way of life. In Faulkner's story, a small boy realizes the wrongness of his father's actions and breaks free of him. Though the ending of the story is ambiguous, it appears that his father has been killed and that the boy will not return to his family. In Wright's story, an African American young man breaks free of the constraints imposed by his family and by society as a whole. The ending is similar to that of "Barn Burning," given that in both cases the protagonist has an epiphany that releases him from an environment in which he has been prevented from being what he wants to be.
So, all four of these stories involve characters (though in situations that are quite different from one other) in which a past life has been superseded. With Hemingway and Fitzgerald, the past was one of a kind of glory, while in Faulkner and Wright it was one of constriction. The question at the center of each of these scenarios is, are these protagonists better off in their new lives?