give someone up for dead
1. Lit. to give up hope for someone who is dying; to abandon a dying person as already dead. The cowboys gave up their comrade for dead and rode off. We gave up the poor old man for dead and went to telephone the police.
2. Fig. to abandon hope for someone to appear or arrive. We were delighted to see you. We had almost given you up for dead. After an hour, they gave up their guest for dead.