。
She stole because of hunger.
Literal
She [topic-は] hunger [because-of-のため] theft [object-を] performed.
盗みを働く is an idiom for 'to commit theft.' The verb 働く ('to work') has a specialized usage with negative-connoted action nouns — 盗み ('theft'), 悪事 ('wrongdoing'), 不正 ('fraud') — meaning 'to commit, to perpetrate.' The pairing feels archaic to learners but remains productive in writing about crime. The phrase ~のため here gives reason ('because of') rather than purpose ('in order to'); both senses share the same surface form. In context, 飢えのため frames the theft as a desperate act driven by hunger — a soft moral excuse rather than a confession.