At the turn of the 19th and 20th centuries, Herbert Hoover was chief engineer for the Chinese Bureau of Mines, general manager for the Chinese Engineering and Mining Corporation, and later the lead engineer for Bewick, Moreing & Co. He and his family lived in the foreign concession zone in Tianjin, which came under attack during the Boxer Rebellion. When the Boxer and Qing armies were bombarding the concessions and placing it under siege, the Hoovers provided great assistance to the Eight Nations armed forces relieving the city - Hoover used his knowledge of the area to guide British, French, Japanese and American troops towards the South Gate of the city while his wife helped care for the wounded, and at one point fought using a .38-caliber pistol with skill. Then, even after given the chance to leave the city to safety at the Taku Forts, they still chose to stay behind to keep helping the wounded.
Suppose Hoover was killed by a Qing sharpshooter while guiding the Allied troops. What would be the major ramifications? Besides the position of 31st President needing to be filled it's important to remember that Hoover also did many significant things before then - by 1914 he had amassed a wealth of $4 million due to his role as a mining magnate, he headed the American Relief Association during WWI to help feed the hungry, became Secretary of Commerce under the Harding and Coolidge administrations, etc.
So...what then?