In Requiem for a Nun, Faulkner writes, "The past is never dead. It's not even past." Much of his work, including this short story, offers a meditation on the past, and the narrative structure reflects that. As a Modernist, Faulkner also tends in his work to explore non-linear time.
In "A Rose for Emily," it is somewhat misleading to think of this story as a story about Emily Grierson. It is much more about the act of narration and the implied audience of the story. The narrator is unfolding this horrific story about a town's legendary character, and the reader stands in for that auditor. A reader response critique can explore that more fully, but as is the case in any dramatic monologue, the implied experience of the teller and the hearer adds a depth. This is especially true as the story is past tense and the "unspeakable" ending has been awaiting discovery all along.
Without the framing device in which we enter the past from the present time, the disturbing brilliance of the story would be lost. Like the South who knew its own decay but denied it, Emily and the town also live amidst its rotten past. The story brings that vividly to the reader, who must reconstruct the story's time line but then realizes that the grim truth of Emily's life should have been obvious to anyone not actively seeking to deny it.
The following order of the story maps out Emily's life chronologically.
1. Emily is a young girl/woman with a father who parades her around town and denies her opportunity to marry.
2. Her father dies and she is unwilling to acknowledge the fact or deal with the dead body for three days.
3. Emily has an independent maidenhood, indulged by the elders of the city who remember an earlier grandeur. This period includes a brief stint giving china painting lessons and a brief romantic attachment to Homer Barron, which seemingly leads to a marriage proposal (hence the silver toiletry set).
4. The town and her cousins express scandalized horror at the thought that Emily might marry a Northerner; Homer leaves.
5. Homer returns.
6. Emily buys rat poison despite being unwilling to offer a good reason for her need to do so.
7. There is a terrible smell that the town attempts to deal with.
8. Emily dies.
9. The town discovers that Emily had slept in the same bed on which the corpse of Homer was lying.