Life is a state, a condition, that can be enjoyed forever. Death is merely a momentary transition from one kind of life (body and soul) to another (soul with no body). Perhaps someone could be eternally dying, but the word death doesn't imply anything more than having a soul, but not having a body.
I suppose you could say that death is this condition of having a soul but not having a body, and I suppose this could be eternal.
Eze_18:4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die.
Eze_18:20 The soul that sinneth, it shall die.
Mat_10:28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
There is no life possible without God. Sin can not live in the presence of a Holy God. There is no such thing as a living body without a soul. Both are required for there to be life. Adam was a soulless body before God breathed life into Him.
Gen_2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Ecc_12:7 Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
Joh_5:29 And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.
Without a soul you are dead---there is no bodiless soul tormenting in hell forever. God returns His breath if life to the lost when they are resurrected unto punishment. When they die, that spirit returns to Him again, permanently. They die the 2nd death.
Rev_2:11 He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.
Rev_20:6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
Rev_20:14 And death and hell were cast into the lake of fire. This is the second death.
Rev_21:8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.