Emily is a tradition in the town. The way she is regarded, and exceptions made for her show this. The town felt that she was "a tradition, a duty, and a care " that had to be upheld. When the smell was getting overwhelming, the town would not ask her about it, because first, it was Miss Emily, and second, she was a lady.
When she died and they discovered Homer, they took care of the situation, saving Miss Emily's reputation.