Miss Emily is an old-school Southern belle trapped by a society bent on forcing her to stay in her role...and an abusive father bent on forcing her to obey his will.
Aww...poor Miss Emily!
But Miss Emily is also a sociopath who kills her fiancee with rat poison, plays dress-up with his corpse until he starts to decompose, and then continues sleeping next to his moldering skeleton until she dies.
Oh. Poor Miss Emily?
Let's first channel our energies on analyzing Miss Emily as a truly tragic figure.
As far as we know, Emily is an only child. (The story doesn't mention any siblings, and just like it never mentions her mother.) The narrator wants to emphasize just how much Emily was her father's daughter, and just how alone she was with him when he was alive. From all evidence, her father controlled her completely until his death, and even continued to control her from beyond the grave.
By separating her so severely from the rest of the town when he was alive, going as far as to make sure she didn't have any lovers or a husband, he set her up for a way of life that was impossible for her to escape. The bare sketch we have of her father shows a man who was unusually controlling, domineering, and capable of deep cruelty, even toward his only daughter.
In fact, it's suggested that Miss Emily's father is so abusive that Miss Emily develops Stockholm Syndrome. When he dies, Emily refuses to believe that he's gone—she almost forbids the townspeople from taking his body away.
She told them that her father was not dead. She did that for three days, with the ministers calling on her, and the doctors, trying to persuade her to let them dispose of the body. [...] We remembered all the young men her father had driven away, and we knew that with nothing left, she would have to cling to that which had robbed her, as people will. (2.13-14)
But her father isn't the only thing holding Miss Emily back. She's also constrained by the demands of society—a society that proclaims that women are weak and feeble and unable to defend for themselves. Had she lived in a more evolved society, the death of her abusive father could have meant freedom. But, bound as she is by the social mores of the turn-of-the-century South, she's expected to do one of three things: marry, live off of her inheritance, or kill herself.
Wow. What a choice.
Since she fails to marry, she's plunged into poverty. The town attempts a bit of generosity: they cook up a lie about how she doesn't owe taxes. This is nice...but check out the way the narrator reports this little white lie:
Only a man of Colonel Sartoris' generation and thought could have invented it, and only a woman could have believed it. (1.3)
See, even though the town is being nice, they're only being nice because it's unthinkable that a woman of Miss Emily's social stature get a job and support herself. If Miss Emily were allowed to work—besides hosting the odd china-painting class—she might not have gone so batty.
But instead the society essentially conspires to keep her indoors. Even when she has a flirtation with Homer Barron, everyone seems dismayed—it's not enough that Miss Emily marry, she has to marry a dude who's a well off as her. It gets worse, though: when Miss Emily is seen buying poison, the town thinks she might be planning on committing suicide...and they approve of this drastic action.
So the next day we all said, "She will kill herself"; and we said it would be the best thing. (4.1)
Wow. That's cold-blooded.
So to recap: Miss Emily is kept in isolation by an abusive father, kept out of the workforce and indoors by a restrictive society, pushed away from marrying a poorer man by her relatives and the townsfolk, and then (passively) encouraged to kill herself. No wonder she has a screw loose.
But then again...we're talking about a woman who kills her fiancee and then continues to cuddle his rotting corpse for the next few decades. We're sympathetic, but there are limits to our sympathy.
What's interesting when it comes to Miss Emily-as-crazed-killer is that the same societal sexism that drives the townsfolk to think it's "the best thing" that Miss Emily kill herself also allows her to literally get away with murder. After Homer Barron dies, a mysterious (and disgusting) smell starts coming from Miss Emily's house. Everyone seems to agree that it smells like a rotting body.
But rather than go investigate—even though a man has recently disappeared—the townsfolk decide to keep mum:
"Dammit, sir," Judge Stevens said, "will you accuse a lady to her face of smelling bad?" (2.9)
Yup. The only thing worse than the overpowering stench of decomposing flesh (coupled with the disappearance of a local figure) is insinuating that a lady smell like anything but roses.
Faulkner is no lightweight: he's not condemning or excusing Miss Emily. He knows it's much more powerful to write a deeply complex character—one who's equal parts homicidal maniac and abused captive—than it is to write either a straightforward saint or demon.
Ultimately, it's up to you to pass judgment on Miss Emily...that is, if you can make up your own mind whether she should be pitied or pilloried.