In September 1902, Teddy Roosevelt was in an accident that killed ome of his secret service agents and injured him. His wounds were infected but he recovered without too much trouble and life went on.
Suppose he dies. He has no VP, so his sec of state, John Hay, becomes President under the rules of the time.
However, John Hay had heart problems, and was due to die in 1905, so even if he ran in 1904, he’d die soon after winning.
So, we could end up with a scenario of 3 presidents dying in a short period of time.