In "A Rose for Emily" what's the significance of Miss Emily Grierson being a necrophiliac?
The main significance is the role that her tendency plays in poor Homer Barron's life. She poisons him with arsenic, and then spends the next decades sleeping next to his body. Homer became a victim of her desire to have companionship and comfort, even if it was in the form of his lifeless personage.
I think that the more pertinent question to ask is why she became reliant on using Homer's body for companionship? What is the road that led her to go to these extremes? If you read the text closely, there are clues. She had an extremely protective father, who kept her from developing normal, healthy relationships. The text states that
"None of the young men were quite good enough for Miss Emily and such,"
which indicates that her father kept her pretty sheltered and didn't allow her to socialize and make friends. He was too snobby-he didn't think anyone was good enough to be with his daughter. Because of this, Emily had to rely on him, and him alone for companionship, love, and validation. So, when he died, it was like her entire world shattered. Letting him go meant letting go of her entire universe, her only friend, and her only sense of security in the world. She had a hard time with this. In fact, the text states,
"She told them that her father was not dead. She did that for three days"
before letting people take the body away. Who knows how long she would have kept her father's body there if the town hadn't forced her to give it up?
So, when Homer came along, it was the only other man who had ever paid her attention. She probably envisioned him filling the gap left by her father. When he told her he wasn't interested, she wasn't going to let that happen--she wouldn't be abandoned again. So, she resorts to murder and the subsequent disturbing behaviors.
So, it isn't like she is a "classic" necrophiliac, a person attracted to dead people, she is just psychologically disturbed in the areas of abandonment. She has had traumatic experiences that have led her to believe that it is better to not be alone, no matter what conditions have to be filled to have someone. I hope that those thoughts help a bit; good luck!
Your question assumes that Miss Emily had sex with the corpse in her bed, but I do not think there is any evidence in the text to support that assumption.
What we do know is that the corpse was found in Miss Emily's bed after she died. He had been hidden there all those years during which the townspeople did not enter Miss Emily's house or at least, never went beyond the common rooms of the house.
The better question might be: Why did Miss Emily keep the corpse in her bed? One answer is that this is the only love she ever knew! Her father chased or frightened away all suitors, probably because he expected Miss Emily to take care of him and because there were no suitors he considered worthy of the family's elevated position in the community, a position that had probably deteriorated swiftly after the Civil War.
If we try to put ourselves in Miss Emily's heart and mind, we might conclude that to some degree she lived in a fantasy world, and the corpse in the bed allowed her to believe that she had a normal life and went to bed with a husband every night. Also, since this "relationship" was in defiance of her father's wishes for her, the corpse had to remain tucked away from the portrait of her father, which would be able to "see" her lover.
I suspect that your question is based more upon a desire to demonstrate you know what necrophilia is than a belief that this is what Miss Emily was doing. However, the underlying question, what was she doing with a corpse in her bed, is a reasonable one.