Author William Faulkner is not specific about time in his short story, "A Rose for Emily." The story shifts back and forth sequentially, but her home is "of the lightsome style of the seventies (1870s)," so we know that a number of years has passed in order to age the home. It is true that her taxes were remitted in 1894, and Miss Emily lived for some time after that. However, since Faulkner first published his story in 1930, it is not possible that Miss Emily died in the 1930s or 1940s, as one of the previous posts suggests. Faulkner had no doubt been working on it for some time before that. The exact date is not stated in the story, but we can assume that Miss Emily probably died in the 1920s or slightly earlier.
Faulkner gives his reader only one exact date in "A Rose for Emily." At the beginning of the story, he writes that Miss Emily's taxes were "remitted" in 1894. At this point, Miss Emily's father would not have been dead for long, and the mayor most likely told Miss Emily that she did not have to pay taxes because of her isolation as a single woman and because she represented the "aristocracy" of the town.
Based on that year, Miss Emily meets Homer Barron several years after that--near the turn of the century (1800 to 1900), and has a brief relationship with him before he disappears. At the story's end, as the curious townspeople enter the deceased Miss Emily's room, the narrator states:
"Already we knew that there was one room in that region above stairs which no one had seen in forty years."
The closing off of the room and Emily's house from the town occurred after Homer's disappearance, so you could argue that with adding on the forty years to 1900 (give or take a couple of years) that Miss Emily died somewhere around the late 1930s or early 1940s.
In regards to the last post, just because a work is published during a certain decade, it does not dictate that events in that work cannot take place in the future. Authors often include events that are outside of the publication time of their works (whether those events be centuries early or decades later).
In William Faulkner's short story "A Rose for Emily," Emily is an elderly spinster who dies. She is like a monument to the town's people. She is tarnished and gray much like the once fine but now weather worn house in which she resides. She has been a recluse and has not been out of the house for 13 years. She refuses to pay her taxes and does not allow visitors into her home. Everyone is curious about the condition of her home after she dies. Miss Emily hides herself away after her father's death leaves her poor. However, she has new hope after she meets a man named Homer. He is supposed to be marrying Miss Emily but he is never seen again. It is not until Miss Emily's death at 74 that people learn the truth.
"Up to the day of her death at seventy-four it was still that vigorous iron-gray, like the hair of an active man."