If an essence can cease to exist, then this essence must have emerged into existence. This is because existence for any essence is either:
An essence that accepts cessation can be neither necessary, nor impossible. Which means its existence must be possible.
The existence of an essence that can cease to exist is not necessary. This is because necessary essences do not accept non-existence in of themselves. So if the existence of this essence were necessary, it would not accept cessation.
The existence of an essence that can cease to exist is not impossible. This is because impossible essences do not accept existence in of themselves. So if the existence of this essence were impossible, it would not have existed in the first place (for it to then cease to exist).
Therefore, the existence of an essence that accepts cessation is possible. And existent possible essences are emergent.