According to dictionary.com, necrophilia is an abnormal fondness for being in the presence of dead bodies. I'm not sure what story you are referring to, but judging from your other questions, I going to assume it's "A Rose for Emily". At the end of this story, the townspeople come into a room decorated like a bridal or honeymoon room. They look around and see a decomposed body in the bed and beside it is the indentation of a head and a long strand of "iron-gray hair". Since Miss Emily's hair did not become gray until after the disappearance of Homer Baron, the implication is that she killed Homer ( that's the body in the bed) and then slept with the corpse. The reference to necrophilia implies that Emily was attracted to Homer's body. However, calling her a necrophiliac may be going a little too far. It seems she wanted only to keep Homer's body to keep up the pretense in her mind that they were married. She seems to have no other attraction in the story to any other dead body.