How does the fur contribute to the theme of the story?

The fur symbolizes Miss Brill herself by the end of the story: she too returns to her small, dark apartment and recognizes that she is shabby and old. The "crying" she imagines coming from the box could be interpreted as Miss Brill herself crying.

The Main Theme:

The central theme of "Miss Brill" is the pain of loneliness, and inadvertent attempts to experience life through the experiences of total strangers.

Explanation: it contributes to the overall integrty of the of the story therfore giving more depth about the story telling us more about the theme