I think the concept of isolation is most clearly reflected in the life of the protagonist of this excellent short story, Miss Emily herself. Throughout the story we are shown that she lives a life that is separate from the rest of the town, and that especially in her last few years, hardly anyone saw her at all. Note what we are told in the first paragraph of the story about how isolated Miss Emily was as a character in her life:
When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one save an old manservant--a combined gardener and cook--had seen in at least ten years.
So, whilst it is clear that her last years were spent in isolation, when we reflect on the dominating memory that the townspeople have of her childhood, it becomes clear that her father ensured that she was kept isolated as well, and that she was never able to form any meaningful relationships because of his idea of their social status. Likewise, the descriptions that we are given of Miss Emily in her old age, when the Aldermen go and visit her about the question of her taxes, indicates that in a sense she is already dead and separated from the rest of the world through her appearance, which is described as being "bloated, like a body long submerged in motionaless water." In every sense of the word, Miss Emily is a character who is isolated.
Miss Emily is a woman who had the whole town wondering what she was doing, but did not allow anyone the pleasure of finding out. Once the men that she cared about in life deserted her, either by death or by simply leaving her, she hid out and did not allow anyone to get close to her. Miss Emily was indeed afraid to confront the reality that Backman discusses. Since she did not want to accept the fact that the people she cared about were gone, she hid in her house and did not go out. She was the perfect example of a woman isolated by a society controlled by men who make trouble for her instead of helping her.