Where is there symbolism in "A Rose for Emily"?

Miss Emily Grierson's home is, in many ways, symbolic of Miss Emily herself. The narrator says of the house,

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.

Miss Emily is outdated, old-fashioned; she does not make sense anymore, and she makes less and less sense as the years pass. The house is likewise dilapidated, and growing more and more so, and it seems to become more rapidly out of place as the world around it changes. It is described as possessing a stubborn and coquettish decay, a phrase that also seems to describe its owner. She is likewise stubborn. For example, when she is approached by the new generation of town authorities, she refers them to the ten years-dead Colonel Sartoris for proof that she does not pay taxes in Jefferson. Further, the reference to coquetry personifies the home as being flirtatious in an antebellum lady sort of way, just as Miss Emily seems to carry herself very much as a similar kind of lady (despite the fact that the war is long over).

Symbolism is a literary device in which a writer uses a concrete object to represent an abstract idea. While not all writers use symbolism, Faulkner has chosen to employ symbolism in at least seven different ways in “A Rose for Emily.”
1. Dust: Dust can be symbolic of many things: neglect, aging, things that are overlooked, and/ or the biblical concept of ashes to ashes, dust to dust. There are seven different mentions of dust throughout the story. Here is an example of those instances:
It smelled of dust and disuse—a close, dank smell. The Negro led them into the parlor. It was furnished in heavy, leather-covered furniture. When the Negro opened the blinds of one window, they could see that the leather was cracked; and when they sat down, a faint dust rose sluggishly about their thighs, spinning with slow motes in the single sun-ray. On a tarnished gilt easel before the fireplace stood a crayon portrait of Miss Emily’s father (I.5).
2. Rat/ Snake: Both of these animals are associated with conniving and dishonesty. The druggist offers Emily “rat” poison.
“I want some poison,” she said to the druggist. She was over thirty then, still a slight woman, though thinner than usual, with cold, haughty black eyes in a face the flesh of which was strained across the temples and about the eye-sockets as you imagine a lighthouse-keeper’s face ought to look. “I want some poison,” she said.
"Yes, Miss Emily. What kind? For rats and such? I'd recom—” (III.33-34)
Later, the townspeople begin looking for the source of the terrible smell emanating from Emily’s home:
It's probably just a snake or a rat that nigger of hers killed in the yard. I'll speak to him about it (II.20).
3. Iron: this metal is associated with being cold and inflexible. Emily’s hair is described as “iron gray.”
When we next saw Miss Emily, she had grown fat and her hair was turning gray. During the next few years it grew grayer and grayer until it attained an even pepper-and-salt iron-gray, when it ceased turning. Up to the day of her death at seventy-four it was still that vigorous iron-gray, like the hair of an active man (IV.48).
4. Black: The color black is associated with death and funerals, but it also has a more abstract meaning of being psychologically “dead.”
Emily is described as “a small, fat woman in black” and she has “cold, haughty black eyes” (I.6, III.34).
5. Closed houses or rooms: There is a psychological component to doors shutting and rooms being sealed off. Here are two examples of “closing” in the story:
The Negro man went in and out with the market basket, but the front door remained closed (IV.47).
From that time on her front door remained closed (IV.49).
6. Barron: Homer’s last name is “Barron.” If the vowel is changed to an “e,” his name can take on a new meaning. If something is “barren,” it cannot bear fruit. Therefore, the relationship was doomed before it began. His first name may also be a clue as to his nature; perhaps this Homer has something in common with the ancient Greek master in that they both spin stories.
7. Rose: There is no “rose” in “A Rose for Emily.” Using this symbolic flower in the title may conjure up some abstract meanings, including love but also, due to its strong scent, may hint at death. The tradition of bringing flowers to a funeral comes from the need to cover the smell of decay.