What is the theory behind this saying: "While Emily had preserved Homer, the community had preserved Emily"?
I like this statement. It seems to sum up the whole story. Emily kept Homer's body in a pristine, though dust-covered, room. Likewise, the whole town kept Emily in a pristine state of denial. The Board of Aldermen didn't try very hard to get her to pay taxes. Sending her a notice every now and then accomplished nothing. By cleaning up her yard at night, the town people let her live in denial of the horrible smell. At least someone tried to help her by writing to her cousins about how Emily rode around town with Homer Barron. But couldn't they have said something to her? Or to him? Were they just trying to stir up some trouble to give themselves a little more to gossip about? Why didn't anybody try to get into her house when she was so sick just to see if she needed anything? I think she entertained the townspeople so much with her eccentricities that they really didn't want her to change. Even after death, she left them a lot to talk about!
The statement carries quite a bit of irony in that "preserved" carries multiple and conflicting meanings. Emily "preserves" Homer's body literally--she keeps it with her--first by murdering him and then by not burying him, and in doing this she "preserves" his place in her life. The town "preserves" Emily by keeping alive (while resenting) her place in the community as a lady and daughter of an important and powerful man, yet that preservation ultimately "kills" her ability to live as an authentic human being. Thus, in referring to each character, "preserve" involves both continuance and termination, both life and death.
Emily kept her perception of Homer alive, at least in her own mind, all the while his rotting corpse laid in the bed that she slept in for many years. Because of her place in the community, that of an aristocrat, she was able to cover up the murder. The communities own perceptions of Emily allowed her to do this. She was more or less a landmark to them.