Faulkner opens his story by telling us that the whole town turned out for the funeral of Emily Grierson. He says that the men, as opposed to the women, who came "mostly out of curiosity to see the inside of her house, which no one...had seen in at least ten years", showed up "through a sort of respectful afflection for a fallen monument". Miss Emily has been a part of the town and its makeup for very a long time, having become "a tradition, a duty, and a care, a sort of hereditary obligation on the town". As such, she personifies a dominant theme in many of Faulkner's works - the slow decay and dying of the Old South. The men of the town feel the sense of her significance in this regard, and attend her funeral out of obligation and respect for a disappearing way of life as much as for Emily as an individual.
(all quotes from Section I)
The story started by the introduction of the funeral of Emily Grierson, where the whole town attended her funeral. The reason for the whole's town attendance out of respect for Emily, was to snoop inside her house. Her death synbolizes a passing of a genteel way of life, which is replaced by a new generation's crass way of doing things.
They went to her funeral out of a respect of an individual, which could be seen:
". . . the men went through a sort of respectful affection for a fallen monument."
telling us about the affection of the people towards her and she really deserves this honour and everything bestowed towards her.