The conflict that contributes to the tension in William Faulkner's story "A Rose for Emily" is the enigma surrounding the life of Miss Emily as an eccentric and antiquated character within a place which is changing towards the future.
This enigma permeates the story, and colors the character of Emily in a diversity of shades: scary, strange, mysterious, sad, melancholic, lonely, haughty, and stubborn. Although nobody really knows Emily personally, the townsfolk narrator offers all of these descriptors as the observations that the people from Jefferson have bestowed upon Emily based merely on either hearsay, or on the rare instances when they are able to take a glimpse of this interesting woman.
Along the narrative we realize that Emily's life has not lacked obstacles: her father dominated her, and his death crippled her mentally. She is also limited by the fact that she once belonged to a good, aristocratic background only to have fallen from grace with the passing of time. Moreover, Emily is unable to change. If anything, the biggest obstacle that Emily has in life, is herself.
However, happy tidings did go her way with the entrance of Homer Barron into her life. As the narrator says, the people actually felt shocked but happy to know that Miss Emily has found a companion. A man whom nobody liked, Homer was still seen as company for an otherwise lonely woman.
Yet, the enigma of Emily comes to a boiling point when a strange smell begins to emanate from her home. After the town's aldermen just went and took care of it, it is said that Emily rarely ever left her home again. In the end, the narrator explains, Emily's death resulted in the first time that the people could actually enter her home. There, they saw that in one of the bedrooms the corpse of Homer Barron had been laying dead for years and that Emily had been sharing the bed with such a corpse. Hence, it is this discovery that ends the enigma that constitutes the conflict and point of tension of the story.