I don’t know if Vatican II ever made such a statement (my guess is no).
It’s a pretty general statement that could apply to anything. Being apart from God, or trying to work apart from (or against God) does lead to death, because only God gives life.
There’s a similar concept that I’ve heard it before from Religious. In times of need, the Spirit raises up groups to perform a specific task. Sometimes the need for that group has disappeared and the Spirit lets that group gradually disappear (as in there will be no more vocations to that group) as other groups are raised up.
This is more of a recognition that the work they were raised up to do has ended, and instead of trying to morph it into something “relavent” they recognize that it is simply time for it to end.