It is said that when Yi fell in the battle his sons took up the helm of the ship he was captaining, how did people not notice Yi was dead and lose morale.
Pretty sure his son and nephew took his place and did as he would have done. Nobody else was around to see him die except them (I think) and they made sure nobody knew until the end. Even the Chinese commander assisting the Koreans did not know until Yi's son came in his stead in response to his calls for thanks/celebration.