While Garfield’s shooter was executed for killing him, you’re right, the bullet didn’t kill him. His doctors did by probing the entry hole with non-sterile instruments and their own dirty hands. Unfortunately antibiotics were a few years off.

The next president to get shot, William McKinley, suffered a similar situation. He was shot at the Pan American Exposition in 1901. It was a huge world’s fair type of thing. One of the attractions at the fair was a new device called the X-ray machine. People were walking around with novel photos of their insides. Nobody had thought about using it as a medical device, so they didn’t X-Ray McKinley and he died. Modern docs say he might have been saved if they’d known where to look.

Hope this helps! — TT