The main idea in a story or any other literary piece is the central thought or most important concept that the author conveys throughout. All the details of the written work therefore relate to the main idea and can be seen as accessories or contingencies that either extrapolate, develop, or provide emphasis in support of the central idea.
In "A Rose for Emily," the main idea is, most obviously, the inability or refusal of the protagonist, Emily Grierson, to accept and adapt to change. The fact that the narrator refers to her as a "fallen monument" symbolizes precisely what she represents—a stubborn memorial to the past.
Miss Emily's actions throughout the story provide ample proof of this. Firstly, there is her unwillingness to pay taxes. She focuses on a privilege given to her father by one who has been dead for a long time. Even though Colonel Sartoris had extended the non-paying tax privilege to her father in perpetuity, it is obvious that such a ruling could not be permanently sustained. Miss Emily, though, refuses to budge.
Another example of her stubborn adherence to the past is the fact that she cannot not accept her father's death. She tells people that he is not dead and holds on to his body for three days before releasing it for burial.
In addition to that, it becomes apparent that Miss Emily hardly ever buys anything new or cleans her house. Her fear of change probably stops her from desiring her place to look brand new or, at least, clean and well cared for. The following extract most adequately declares this fact:
...only Miss Emily's house was left, lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps—an eyesore among eyesores.
The most profound example of Miss Emily's refusal to let go of the past lies in the treatment of her supposed sweetheart, Homer Barron. It is common knowledge in the town that he is not the marrying kind and prefers the company of men. When he disappears, everyone believes that he has left her. The shocking discovery in an upstairs room of her house, however, proves otherwise. They find Homer's extensively decomposed body in the bed and discover, on a pillow next to his, a long strand of Miss Emily's hair.
It is pertinently obvious that Miss Emily murdered Homer with arsenic that she bought from the shop about thirty years before. She has been keeping his body for company through all the years. It also seems that she has either occasionally or constantly been sleeping next to it.