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A coward dies a thousand deaths, a brave man but one. Surrender seems to infer that some fight, conflict, war, or confrontation has taken place. A coward usually won't allow himself to become a part of the fight, so there's no reason to ask for terms and surrender. You ask to what or whom do you surrender. If I've fought well and come to the realization that further fighting is to no avail, then I'd ask for terms and take what's coming.
