Another way to look at the townspeople referring to Emily as "poor Emily" is that they did not attempt to really try to understand what was behind her strange behavior. They, in my opinion, judged her unfairly.
People tend to dismiss others that they do not understand or they pity them. People also tend to dislike people or things they do not understand. This is what I think happened to Miss Emily. Based on rumor, the townspeople tended to simply feel sorry for her/pity her/dismiss her as crazy.
The first time the people speak of feeling sorry for Emily is after the incident in the part two of the story "A Rose For Emily" where the town residents begin to complain about the smell the men go to her house and spread lime around. The smell goes away. Faulkner then writes " That was when people had begun to feel really sorry for her. People in our town, remembering how Old Lady Wyatt, her great-aunt, had gone completely crazy at last, believed that the Griersons held themselves a little too high for what they really were. None of the men was quite good enough to Miss Emily and such."
In part IV the narrator states, "Thus she passed from generation to generation--dear, inescapable, impervious, tranquil, and perverse," thus defining why Emily is "poor."
She is "dear" and "inescapable" because she is a "tradition, a duty, and a care." In the old aristocratic society people looked up to those of higher social class and old, established families regardless of their idiosyncrasies, much like the respect that Pip's sister, Joe, and Uncle Pumblechook showed Miss Havisham despite her strangeness and decay.
In part III the townspeople first use the term "Poor Emily" after she falls from social standing by courting a Northern laborer: "even grief could not cause a real lady to forget noblesse oblige." Yet, Emily cares her head high and is "tranquil" as a lady would be, dismissing the men who come to collect taxes in the belief that her father still wields political power: "Perhaps he considers himself the sherriff..." she haughtily refers to the town official." This imperviousness in the face of change is another way Emily is "poor."
With Emily's rejection of the New South, Emily acquires a perversity as she begins to live in a world created by her own mind, her woman's life "thwarted" by the father. Unable to deal with reality, Emily creates one of her own by halting time in the poisoning of her lover.