I would say that one aspect of society that has to be included is that Miss Brill lives in a world of her own. Her world is outside social conventions, as she is not fully in touch with such realities. There is a massive chasm between what society sees her as and what she sees herself as. In this light, I think that the reader has to fully grasp how this disconnect plays into her own condition. When Miss Brill sits in the park, conducting the band and believing that the entire world is for her, conceiving herself as the center of being in this universe, one grasps that she is either not entirely in synchronicity with reality or extremely narcissistic. The theme of illusion and reality is enhanced with such an understanding. In the final analysis, this disconnect is what the reader is left with at the end of the story. There is little in way of bridging this divide as there is not a clear statement that Miss Brill fully grasps what reality is and her place within it. She blames the stole for her condition.
Miss Brill is one of those members of society who are often invisible to others. So, when considering Miss Brill vs the society in which she lives, one must consider the things about a society that allows lonely individuals such as Miss Brill to become alienated in the first place.
Things are not what they seem in this story. Miss Brill believes she is an important part of the "play" that is enacted in the park every week, that she would be missed if she did not show up. This proves not to be true. She believes she looks dashing and smart with her little fur, but in reality, the others in the society believe she is comical and pitiful. In reality, she is a lonely woman trying to pretend that she matters. Why is she lonely? Where is her family? How can a society allow this to happen? Why doesn't society provide fellowship for lonely individuals such as Miss Brill? Instead, society spits on them because they don't conform, because they are different - old, for example. In a sense, Miss Brill is living in a metaphorical cupboard similar to the one in which she stores her little fur.