When you refer to William Faulkner's "A Rose for Emily" and its non-linear plot structure, I expect that you are referring to Faulkner's choice not to present the story in a chronological fashion. In that the story itself is especially macabre, I find that this structure underscores the unusual series of events that direct the plot to its eventual conclusion. However, it is also Faulkner's unusual organization of these events that allows him to so masterfully surprise the reader by the end of the story.
The story is told by the narrator through a series of non-sequential flashbacks.
As the author introduces Miss Emily, she is already old. We discover through flashbacks that turn back time—and swift jumps back to the present—why Emily no longer pays taxes and how her father treated her. We also learn about how she changed when her father died and sent her female "relations" packing—establishing Emily as an independent woman well ahead of her time. We are introduced to her behavior that raises eyebrows, and then to her romance with Homer Baron. Next she is sick for a time; there is an awful smell around the house; and, we read that people haven't seen much of Miss Emily since she stopped giving china-painting lessons.
This structural style Faulkner adopts is much like a "shell game" (also known as "three shells and a pea"), when a pea, for example, is placed beneath one of three walnut shells—we are challenged (as the shell's movement shifts back and forth) to see if we can follow the action and without getting "lost."
Had these events been presented in chronological order—and had Faulkner's imagery been any less dramatic and intriguing—we would not have been as nearly as surprised as we are when he delivers the last few details of the story that "scream" out on the page, while silently conveying the horror we draw from the author's inferences:
Then we noticed that in the second pillow was the indentation of a head. One of us lifted something from it, and leaning forward, that faint and invisible dust dry and acrid in the nostrils, we saw a long strand of iron-gray hair.