In Faulkner's "A Rose for Emily," characterization of Emily Grierson is accomplished through the speaker, who represents the townspeople. The town, including Emily, is attempting to survive in the post-Civil War South. Emily would have grown up in the ante-bellum South--before the Civil War devastated the South's economy--part of a fairly wealthy family. Emily, indicative of many people in the South during that time, has trouble letting go of the past.
In fact, saying she has trouble letting go of the past is probably an understatement, as we read after we are told her father dies:
The day after his death all the ladies prepared to call at the house and offer condolence and aid, as is our custom. Miss Emily met them at the door, dressed as usual and with no trace of grief on her face. She told them that her father was not dead. She did that for three days, with the ministers calling on her, and the doctors, trying to persuade her to let them dispose of the body. Just as they were about to resort to law and force, she broke down, and they buried her father quickly.
We see her resistance to change again when the town is offered free mail service, and she "refused to let them fasten the metal numbers above her door and attach a mailbox to it. She would not listen to them."
Of course, the most important example of Emily refusing to let go of the past and trying to hold on is her poisoning of Homer Barron. They take rides in the country and spend time together, but Homer, the narrator says, is not the marrying kind. Emily, apparently, refuses to let him go and poisons him with arsenic in order to keep him with her.
Ironically, Emily may actually believe Homer, as she says she believes of her father, is not dead. If so, her mind truly is a mind that clings to the past.
Emily Grierson appears as a lonely, sad embittered old woman who has lost track of reality. She still seems to hold on to some shreds of self-esteem however, as she is clinging on to the past and what she feels should be her status of prestige in the town. Emily is probably harking back to the days when her family was important in the neighborhood, so much so that no-one had the audacity to come after the family for their taxes. Even though most of Emily's family's fortune is now lost, she has not taken on board the reality of the change in circumstances, so the dignitaries of the town make only feeble attempts to get the money - probably out of respect for her late father. Emily meanwhile becomes a social isolate, becoming more and more disocciative every year - the only exception is an unrealistic attacment to a man who is not even attracted to women.
Emily Grierson is the daughter of former leaders of the town of Jefferson. We learn that when her father died she was left virtually destitute. At one point she was forced to the necessity of teaching pupils to paint china. Nevertheless, the deputation of alderman treats her with the respect that was in the past due to her position and prestige in the town. Thus Emily’s position of eminence has not changed, at least in the public eye. Later on, she courts a road paver, Homer Baron, whom does not return here affection for him since he is homosexual. We also later learn that Emily has probably poisoned Homer. She is then found dead in her upstairs bedroom at the end of the story.