Does annihilationism mean that people cease to exist?
The fact is, there are often two different meanings of existence and the ceasing thereof at play when this question arises. For that reason, it is important that we define our terms and not equivocate.
The First Definition
The first idea involves a sort of brute, cosmic obliteration that destroys even the atoms a person was made of. Annihilationism does not necessarily deny this sort of ceasing to exist per se, but at the very least, this sense of complete annihilation is not necessary for evangelical conditionalism or annihilationism to be true.