Symbolism, Imagery, Allegory
We can't say that Bibi's illness is a metaphor exactly, or for that matter, even a symbol of anything. In fact, it's a good example of what Lahiri likes to do with things that ought to be metaphors, symbols, or whatever. She puts them to work.
Let's take Bibi's illness as an example. Bibi's illness is Bibi. Okay, so we guess that's more or less a metaphor, or better yet, a metonym.
But that's not what's important. Bibi's illness gives her something to talk about, to socialize with; it makes people notice her: "She bemoaned her fate and challenged her stars as we hung our laundry" (TBH 4); "Each day she unloaded her countless privations upon us, until it became unendurably apparent that Bibi wanted a man" (TBH 5).
It's not like Bibi's illness means anything really grand like "death," "honor," or what have you. It's a conduit, a way for Bibi to be a part of her neighborhood. It keeps Bibi and the story grounded in her community.