What takes place at death is the opposite from what happened during Creation. The body returns to dust and the spirit, or breath, returns to God who gave it. The dead, both righteous and unrighteous, are in their graves and will hear Jesus' voice calling them forth from the grave to reward or punishment. The Bible makes it plain that King David is saved. We are souls, and souls do die.
Man is mortal.
Only God is immortal. The widely believed teaching of the undying, immortal soul is not found in the Bible. The teaching is man-made. Yes, the righteous will be given immortality at the resurrection. The wicked never receive it.