A group of people and myself were playing season of the witch objective 1A and we had to destroy the black book. The investigator who had the black book and alien statue needed was on the brink of death and had three cultists in their space. The problem we ran into is she had to evade to take the action to destroy the black book, however she failed evading and died in the process. The rules say that pass or fail, an action goes through after evading, but it doesn't specify what happens if the person dies in the process and it all came down to whether it went through or not. So does an action go through after failing an evade check and dying in the process.

Nope.