What is Faulkner's primary metaphor in "A Rose for Emily"?

A metaphor is a literary device in which a writer compares two things that seem to have nothing in common but actually do have some similarities. The metaphor Faulkner uses most often compares Emily to a “fallen monument.”
In "A Rose for Emily," the pre-Civil War aristocracy is fading. The old homes are falling into decay and repairs are being neglected. The old ways are being ignored and replaced with new values.
Likewise, Emily is aging. Her slight beauty is gone. No one in the new generation is interested in maintaining the “hereditary obligation with which they have been bestowed" to pay Emily's taxes on her behalf. While Faulkner only uses the words “fallen monument” once, the entire story revolves around this essential metaphor:
When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one save an old man-servant—a combined gardener and cook—had seen in at least ten years.
It was 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 garages and cotton gins had encroached and obliterated even the august names of that neighborhood; 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. . .
Alive, Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town, dating from that day in 1894 when Colonel Sartoris, the mayor—he who fathered the edict that no Negro woman should appear on the streets without an apron—remitted her taxes, the dispensation dating from the death of her father on into perpetuity. Not that Miss Emily would have accepted charity. Colonel Sartoris invented an involved tale to the effect that Miss Emily's father had loaned money to the town, which the town, as a matter of business, preferred this way of repaying. Only a man of Colonel Sartoris’ generation and thought could have invented it, and only a woman could have believed it.
When the next generation, with its more modern ideas, became mayors and aldermen, this arrangement created some little dissatisfaction.
(I.1-4)