"A Rose for Emily" by William Faulkner is a classic example of Southern Gothic literature, which is the style Faulkner is perhaps best known for. Relevant social issues to the story are those of gender, the post-Civil War era, and Southern ideals.
Some of the classic elements of the Southern Gothic style are that it uses supernatural or unusual events and the use of the grotesque, as well as characters who do not fit in with the traditional society. In "A Rose for Emily," Emily Grierson is the grotesque character. Emily was an outsider and something of a spectacle for the town; the townsfolk enjoyed gossiping about her and seeing what she would do next. Faulkner writes in section IV,
"So the next day we all said, "She will kill herself"; and we said it would be the best thing. When she had first begun to be seen with Homer Barron, we had said, "She will marry him."
Here we can see the town gossiping about her. She often behaved in ways that were atypical for a Southern lady of that period; specifically, how she refused to pay her taxes and how she never married. The fact that she never married went against the expected role of a Southern woman—get married and have children.
Also, men were expected to be chivalrous and take care of their women. Homer Barron, however, did not do this. He did not marry Emily (and he paid greatly for it).
Moreover, "the negro," who Emily employs, is another example of how she tries to cling to the old ways of the South by still having an African-American servant tend to her.
The Southern setting is also key in this story. Many houses in the South were large houses like those of plantations and had big front porches with rocking chairs. Emily's house is described as
"...a big, squarish frame house that had once been white, decorated with cupolas and spires and scrolled balconies in the heavily lightsome style of the seventies, set on what had once been our most select street."
But now the house is falling down, which is representative of the old ways of the South falling. The story takes place after the Civil War, and society is changing. There is no more slavery, gender roles are starting to shift slightly, and the culture in general is changing. Emily and the setting are symbols of the Old South that is reluctant to change, even though the change is inevitable.
In other words, both Emily and the setting (the house, the town) are beginning to decay, to exist no more, as the old ways of the South will cease to exist. Decay, of course, becomes most literally represented at the end of the story, after Emily's death, when the townsfolk enter her falling-down house and discover the old, decaying body of Homer Barron, Emily's old sweetheart and the man she had wanted to marry but who had refused her. Thus Emily killed him and kept his body, neatly dressed, on her bed, and she slept next to him at night (which we know because of the "long strand of iron gray hair" found on the pillow next to Homer's corpse). Emily's resisted change to the point of creating her own reality.
All of these issues—social, setting, and decay—are intertwined in the story. They all work to illustrate the decline of the old ways of the South, and this inevitable change no matter how hard anyone tries to cling to the old ways.