Emily's family was evidently once wealthy and prosperous, as evidenced by Faulkner's description of the neighborhood in which the house is located. For whatever reason, Emily is now poor and due to her upbringing, she has no useful skills whatsoever to earn any reasonable income.
However, she comes from an era and region in which it would be improper for a lady of her social class to work. Colonel Sartoris knows she has no money for taxes so he manufactures a tale about the town actually owing money to the late Mr. Grierson, thereby cancelling her taxes. In this way, Colonel Sartoris enables her to cling to meaningless (and unfair) traditions with no consequences. She believes she is exempt from taxes because she is special. When new people are elected to run the town, they have to carry on this tradition because it would be improper to evict a quality person like Miss Emily from her home.
Judge Stevens and the aldermen allow her to get away with murder because it would be rude to confront her--a lady--about the horrific smell coming from her house. Finally, the druggist won't even stand up to her and effectively breaks the law by dispensing arsenic to her without her disclosing the intended use.
Emily Grierson's father greatly influenced who Emily became. Her father was the only male figure in her life. No doubt, he was a good man in many ways; however, because he kept such a tight rein on her and because he did not allow her to have suitors, she was never able to experience love in the way that she desperately longed. Enotes states that "It is his [her father's] influence that deprives her of a husband when she is young." Because of this lack of love, Miss Emily resorted to desperate measures to keep it; for example, she wouldn't allow the townspeople to remove her father's body for several days after his death.
Homer Barron also influenced Emily's actions; unfortunately, he also became her victim. Homer's intentions are never clearly stated (as to why he is "courting" Emily); however, it is noted that "it is known that he drinks with younger men in the Elks’ Club and he has remarked that he is not a marrying man" (Enotes). Perhaps because he would not commit to Miss Emily is why she saw no other option except to kill him in order to be able to "preserve" their love.