In the story "A Rose for Emily" what does Emily represent?

First, Miss Emily is a character, not just a representation of something else, as the story is not a fable or an allegory but a piece of realistic fiction. 

One major theme of the story is the relationship between the "old South" with its aristocratic ideals and social stratification and the "New South," which is much more modern and equal but in some ways more crassly commercial and not without prejudices of its own.

Miss...

First, Miss Emily is a character, not just a representation of something else, as the story is not a fable or an allegory but a piece of realistic fiction. 

One major theme of the story is the relationship between the "old South" with its aristocratic ideals and social stratification and the "New South," which is much more modern and equal but in some ways more crassly commercial and not without prejudices of its own.

Miss Emily comes from a wealthy family and has habits and assumptions based on a certain class structure that no longer exists. She is not really prepared to live in the "New South" and thus is a sort of misfit, but one whose pride in her background and traditions prevent her from reaching out to others in the town for help. While she is in many ways portrayed as a grotesque throwback, some readers also come to admire her indomitable will and ability not to be exploited by Homer.

She can be said to represent the Old Southern aristocracy and its traditions and values.