If war were to break out, what would become of us?

Literal

By-chance war [subject-が] occur-[conditional-たら], we [topic-は] how become [explanatory-のだろう]?

どうなる ('how will [it] become') is the standard Japanese way to ask about an unknown future state — 'what will happen to X?' The のだろう ending is a deliberative, musing question marker: the speaker is wondering aloud rather than directly asking.