Miss Emily is tolerated by the townspeople because she (and her family) has become a kind of monument in the town. The townspeople and the town had changed, but Miss Emily and her house had stayed the same, and the town doesn't know what to do with her. She refuses to pay taxes, she refuses their efforts to interact with her, and she eventually gets to a point where she never comes out. The townspeople just watch her from afar with curiosity. Her family used to be very important in the town, especially her father, but they aren't anymore, and the town just lets her be. The keep a somewhat respectful distance, even though they don't really seem to respect her, because of what her family used to be.
In addition to this well-written answer, Miss Emily represents Southern Tradition. All the townspeople also have this heritage, although they are not all from as affluent families and importance. They respect the icon of the southern lady, and to that end they don't question the "smell" which emanates from her house (we know this later to be Homer's rotting flesh). They just spread lye around her yard to get rid of it. She represents a past of grandeur...much like the life of Hollywood stars or professional athletes hold for regular Joes in the USA. We don't always agree with what they do, but we are enamored with them just the same.