"A Rose for Emily" offers at least a few lessons about the consequences of failing to develop our potential and pursue our dreams. Emily is constrained by her father and then by the ghost of her father. Emily is constrained by the social conventions of the past, as well. Her father finds fault with every potential suitor available, because they are not socially "suitable" for a woman of Emily's class. This leaves Emily with few choices after her father dies, with his portrait still hanging on the wall, controlling her options. As a woman who appears to be financially comfortable, Emily could likely have lived a good life as a single woman, pursing her talents and interests, but societal convention did not allow her to do that, either. Finally, Emily is left with nothing but a corpse in her bed, a symbol, really, of the deadness of what were certainly her hopes and dreams as a young woman, a kind of living death she has lived, unable to love, to marry, to develop in any way at all. And to be sure, she is a rose that has not been able to bloom, dried up before realizing her full beauty as a person.
This may very well be a parable for the South in general, which seemed in many ways unable to move on after the Civil War, still invested in what was perceived to be the glory days of slavery and the societal conventions and limitations of those times. It may not entirely meet the defining characteristics of a parable, though, as explained in the "Parable" link.