The fact that no one checks up on Emily also shows Emily's symbolism in the story. Emily and her family represent the old South when men were gentlemen and woman were ladies. As the next younger generation takes over, they don't have the same feelings of respect toward Emily that the older generation had, like Colonel Sartoris. The time of the old South, with its ways and values, was over, and Emily's isolation and death reflects the decay and death of the old ways of doing things. The new generation of people in the town are symbolic of the new South with new values.
The first paragraph gives initial indication that no one has been willing to check up on Miss Emily. After she passes away, the men mourned her as a 'monument', showing she was quite separate from them, and the women were curious to see inside her house because no one had ever seen it. The discussion of the taxes shows further unwillingness on the part of the town to approach Emily: they try to deal with the situation by sending her notices but are eventually forced to visit.
When the smell begins coming out of Miss Emily's house, no one is willing to approach her about it, so a group of men secretly sprinkle lime on her property at night. And when Emily begins spending an inappropriate amount of time with Homer Baron, the Baptist minister is forced by the town to call on her, but in the end, the town tries to fix the situation again through a letter, this time sent to the Grierson cousins. Continually, these events add up until the townspeople refuse to check up on Emily at all. They simply watch from the outside making conjectures about what might be going on inside the Grierson home.
Faulkner uses these situations to show the old-fashioned, outdated, pride of the Grierson family represented in part by the description of the house: "[O]nly Miss Emily's house was left, lifting its stubborn and coquettish decay ...an eyesore
among eyesores." The family used to be respected and wealthy; now they clung to their old image even in decline.