Miss Emily comes from a privileged family, and the townspeople expect her to therefore behave in certain ways. Because her family has always enjoyed financial success and the respect of the town, they expect that she will follow the characteristically Southern social expectations of their society. Time after time, Miss Emily defies their expectations: she shuts the town out, cuts her hair off, and then does the unthinkable—she begins a relationship with a day laborer from the North.
This is too much. The townspeople begin talking about her noblesse oblige, without directly saying so, alluding to her obligation to continue the social traditions of her family and their society. A woman of status should clearly not be engaged in a relationship with a common day laborer, and the idea is so preposterous that they hope that some member of her family from Alabama will show up to set her straight.
Since there is a rift between Miss Emily's direct family and these relatives in Alabama, it seems that no one can come to "rescue" Miss Emily from her poor choices. Thus, the townspeople are left shaking their heads, muttering "poor Emily" as a response to the way she seems intent, in their minds, on destroying her family's legacy.
Miss Emily continues to "[carry] her head high enough" in spite of the fact that the rest of the town "believed that she was fallen." Though the townspeople may believe that her social defiance negates a privileged social standing, Miss Emily demands the full respect that the last member of the Grierson family deserves.