。
We gave up, figuring he must be dead.
Literal
We [topic-は] he [subject-が] died thing [quotative-だと] gave-up.
死んだものだ uses ものだ ('it is the case that, that's how it is') as a reflective/evaluative ending — here embedded in an 'as if' clause via と思う-equivalent. 'Gave up thinking that he had died' — resigning to the belief. あきらめる ('to give up') captures the resigned acceptance.