How does Emily's character develop throughout the story?
When Emily Grierson was young, her father drove away all of the young men who showed an interest in her, and the people in the town believed that "she would have to cling to that which robbed her, as people will." When he passed away, she would or could not accept it, and she told everyone that he had not died. For three days, she stuck to this story, until, finally, when the town ministers and doctors were about to force their way into her home, she allowed them to take the body. However, "she broke down" when they took him. She seems helpless and weak.
When Homer Barron, a construction foreman, comes to town, Emily seems to take up with him, beginning a relationship. He is someone who her father would have found entirely unsuitable—he's a laborer, he's dark complected, and he's from the North. Emily seems to have chosen someone who is the exact opposite of who her father would have chosen, and this makes it seem like she's trying to punish her father, though he's dead, for his responsibility in her sorrowful solitude. Homer, however, is "not a marrying man," and so Emily, rather than allow him to leave her, as all the other suitors and her father did, kills him in order to keep him. While this isn't healthy behavior, we can see that Emily does gain some agency, she takes things into her own hands—having had everything done for her when her father was alive—and she makes her own decisions. Again, they aren't necessarily good decisions, but they show a change in her: she was once willing to be ruled, but she changes into someone who rules instead.
In William Faulkner's "A Rose for Emily," Emily changes only superficially. In fact, one of the traits that makes Emily what she is is her inability to change.
Emily is a character raised in the ante-bellum South who is trying to hold on to her pre-civil war world. She even refuses to have a mail box installed. She won't let go of her father when he dies until she is forced, just as she won't let go of Homer. If she changes, the change is only that she gets better at holding on to what she wants to hold on to. She understands that Homer is not the settling down type, so she makes a preemptive strike, if you will, and poisons him so that she can keep him with her forever. And she manages to keep it a secret.
She succeeds (by holding on to Homer), where she had failed with her father.
In the short story "A Rose for Emily" Miss Emily is first seen as the mysterious old lady who died alone in her southern home that was once regal but has fallen to waste. The writer then takes us back to a time when she was slender and pert sitting in the carriage next to her father. She was a young southern belle with a proud and prestigious father which gave her the presence of prestige.
As one moves through the story her father dies and she has trouble handing being left alone. She can not accept his death initially, but she finally allows them to remove him. She is left with no money so she finds a way to support herself. However, she does not let go of her ideals that she is still just as majestic as she had been when he father was alive. The house becomes more and more run down and time passes on. People send their children to her for classes just to help her out of pity.
One day a man comes to town and she has the glimmer of hope that he will love and marry her. However, he prepares to leave town. He disappears and the townspeople believe that he had just gone on without her.
Miss Emily is sill headstrong and adamant. She does not allow people into her home. She has become stout and her body has aged and her hair has become an iron gray. After she dies the people enter her home and find the skeleton of Homer on her bed with one of her gray hairs beside it.
Miss Emily has gone from being a sympathetic aging southern belle to a murderer who was mentally off.