Being dead doesn't mean we cease to exist. Dead or alive refers to the condition of our soul's relationship to God. God has power over the life and death of the soul through the sacrifice of Christ on the cross.
Deliver Your Soul From Death
You Can’t Keep Your Soul Alive
The bad news is that you, your own self, can't keep your soul alive. The good news is that it can be kept alive through faith in Jesus Christ.
Alive or Dead?
Paul's writing to people who are metabolically alive and telling them that they were dead and now they're alive, clearly he's not talking about their bodies, he's talking about their souls. We've identified two states of the soul.