There is nothing eternal about man. When Adam & Eve were banished from the Garden of Eden, the reason was because they could not eat of the tree of life and live forever. (Genesis 3:22) Only God is eternal.
Immortal soul is a concept of the Pharisees and Essenes.
From Josephus.
1. Now as to Hades, wherein the souls of the of the good things they see, and rejoice in the righteous and unrighteous are detained, it is necessary to speak of it. Hades is a place in the world not regularly finished; a subterraneous region, wherein the light of this world does not shine; from which circumstance, that in this region the light does not shine, it cannot be but there must be in it perpetual darkness. This region is allotted as a place of custody for souls, ill which angels are appointed as guardians to them, who distribute to them temporary punishments, agreeable to every one's behavior and manners.
2. In this region there is a certain place set apart, as a
lake of unquenchable fire, whereinto we suppose no one hath hitherto been cast; but it is prepared for a day afore-determined by God, in which one righteous sentence shall deservedly be passed upon all men; when the unjust, and those that have been disobedient to God, and have given honor to such idols as have been the vain operations of the hands of men as to God himself, shall be adjudged to this everlasting punishment, as having been the causes of defilement; while the just shall obtain an incorruptible and never-fading kingdom. These are now indeed confined in Hades, but not in the same place wherein the unjust are confined.
Only God can grant life for a soul to live forever, or else a soul is considered dead. "Dead" in definition could mean that an immortal soul remains immortal even in the case that eternal life is not given to him.
Jesus said that God is the God of the living, God is the God of Abraham and Jacob. So Abraham and Jacob's souls are not considered as dead.
From here we can tell that the heavenly definition of dead/alive may be different from what earthly humans defined.