Exposition is defined as...
...the beginning portion of a plot in which background information about the characters and situation is set forth.
The discourse that takes place at the start gives insight into the main conflict of the story: man (or woman) vs. society. The many questions that surround Miss Emily Grierson are the result of a disconnect...between Miss Emily, who has become a recluse, and the town who knows something about her younger years, and next to nothing thereafter.
When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one save an old man-servant—a combined gardener and cook—had seen in at least ten years.
In William Faulkner's "A Rose for Emily," the style the author adopts not only provides us with information, but also keeps the reader unbalanced throughout the story by using flashback and foreshadowing. The tale actually starts very nearly at the story's end, an interesting choice. The author introduces the story's conflict in the first sentence: not that Miss Emily has died, but how she is perceived by society—the men come from respect and the women from curiosity. No one comes with a sense of love or friendship. The first sentence also presents the long-standing separation that Miss Emily has maintained for many years from society.
It is this separation, along with the style the author has adopted, that allows Faulkner to weave such an intricate and macabre tale. Because the town has been mostly unaware of Miss Emily's actions for many years, except for what little they have seen, heard or observed in the behavior of her house servant, much of Miss Emily's life is a mystery. This design is perfect for taking the reader very much off his or her guard with an ending that is quite unexpected.
The exposition adopted provides the reader with the sense that much is unknown about Miss Emily.
Another example of man vs. society comes with the knowledge that, in life, Miss Emily was a force to be reckoned with—one the men of her society had never been able to control. The exposition also foreshadows the final example of this conflict in Miss Emily's power to "vanquish" society one last time upon her death, when the townspeople open the bridal chamber upstairs:
Upon a chair hung the suit, carefully folded; beneath it the two mute shoes and the discarded socks.
The man himself lay in the bed.
Not only do they find that Miss Emily killed Homer Barron, but that she slept beside the dead body, even when she was elderly (many, many years after his disappearance), proven by the color of her hair:
One of us lifted something from [the second pillow], and leaning forward, that faint and invisible dust dry and acrid in the nostrils, we saw a long strand of iron-gray hair.
The conflict is never resolved. Introduced as a worth adversary at the beginning of the story, by the end Miss Emily has still had her way. As far as the murder is concerned, she is well beyond the arm of the law when the body is found, and still something of a mystery.