The story
From the maritime tradition that a sea captain holds ultimate responsibility for both their ship and everyone embarked on it, and in an emergency will either save those on board or die trying.
Etymology from Wiktionary, CC BY-SA 4.0.
the captain goes down with the ship
Today it means: A leader is ultimately responsible for the penalities of a catastrophe, even if they result from external causes or the misactions of others under the leader's purview. Full definition →