For an immigrant, the difficult journey to America is only the beginning of a long, arduous journey as a foreigner here.
It's important to notice how much the families in the Vietnamese immigrant community depended on each other. For instance, when the neighborhood boys are caught misusing the pool, the entire apartment complex loses the privilege of having a pool.
This is an indication that as refugees and immigrants, the individual families often don't have enough financial stability to veer very far from when they started. When the narrator, understood to be the author herself, manages to live as a successful author on the other side of the country, this is taken as the final stage of the transition of immigration. In other words, her parents don't really benefit nearly as much from their sacrifice as the child does.
America is often brutal, and is not utopia.
The kind of work that is available to immigrants like Ba are often very difficult and not very stable. This means that the family is condemned to exist as foreigners, and also as debtors in the working class. The main symbol for America is a landlord, and not only a landlord, but a man who ends up being arrested for actual murder. That's the lasting impression the narrator gives us of her childhood as an immigrant—parents who were never allowed to relax, because their new culture was hostile and demanding of them.
Maybe it's not her parents fault that they argued so much.
This is an implicit theme in the novel. When the narrator allows the reader to see what are actually some gnarly private family troubles, she invites us into a question about the cause of the constant violence and agitation that defined her young life.
Is it because her parents are evil people? Well there is some question about the morality of the father, a veteran for a brutal war, and quite possibly a former career criminal, but actually, no—the novel doesn't blame them for things. Instead, the narrator shows frequent reminders of Vietnam, reminding the audience of their refugee status. In other words, maybe part of the sacrifice the parents make when fleeing to America is their happiness and their interpersonal relationships.
Pursuing a future for one's self after a difficult childhood usually means abandonment of the family.
When the novel ends, it ends on a terribly sad note. The parents are still locked in their daily struggle, still avoiding debt collectors, but the daughter is now a famous novelist, the author of this book, most likely. To them, she is a rumor among the neighborhood, and they constantly hear reminders of her success, but she's not there anymore to help them, and they're suffering without her.
