How is it possible that James Brady died from a gunshot wound he sustained more than thirty years prior to his death?

The death was ruled a homicide by the coroner, but without any published chains of causality. What is known is that Mr. Brady has suffered many different ailments and after-effects from the shooting including issues with his brain and blood clots likely caused by the fragments of the bullet still lodged in his skill. He need regular care as well as multiple operations.

As such, it is almost certain that Mr. Brady's death was hastened by the shots and the ill health he endured over the decades thereafter, but no direct, proven causality with a single reason was published in the coroner's report. For the verdict to be "homicide", however, it is enough that the wounds sustained caused an earlier death than would have been natural.

https://www.theatlantic.com/national/archive/2014/08/james-bradys-death-ruled-a-homicide-33-years-after-he-was-shot/375818/