。
She spoke on behalf of homeless people.
Literal
She [topic-は] house-not-have-people [of-の] proxy-speech [object-を] did.
Two compounds give the sentence its shape. 家のない人々 = 'people without homes,' built as a noun-modifying clause around the existential ない: literally 'people for whom houses do not exist.' Inside the relative clause the existential subject 家 takes の rather than が — the standard が→の swap available in noun-modifying clauses. 代弁 is a Sino-Japanese compound: 代 ('replace, substitute') + 弁 ('speech, advocacy') = 'speaking for, by proxy.' Together they form a tidy advocacy frame in formal register.