The Bible calls this final separation from God “the second death.”
Isaiah 59:1,2
1Behold, the LORD'S hand is not shortened, that it cannot save; neither his ear heavy, that it cannot hear:
2But your iniquities have separated between you and your God, and your sins have hid his face from you, that he will not hear.
In the Book of Revelation the lake of fire is so described (Revelation 20:14). Jesus also identified Gehenna as a second death when He warned: “Do not be afraid of those who kill the body but cannot kill the soul. Rather, be afraid of the One who can destroy both soul and body in hell [Gehenna]” (Matthew 10:28; see also Luke 12:4,5). This clearly refers to another death after the physical death of the body.
It is also clear that this death is different in order and in kind. As physical death is separation from the body and from the environment of this life, so the second death is a final and eternal separation from God and from the life to be enjoyed in the new creation.
Among those consigned to this second death will be all who take the mark of the beast (Revelation 14:9–11). These will be tormented with fire and brimstone in the presence of the angels and Christ. That is, though shut off from the new creation in the lake of fire, they will be able to see the Lamb of God they rejected
just as Lazarus was able to see across the great gulf between Hades and Abraham’s bosom (Luke 16:23).
Again, they will not be annihilated, for “the smoke of their torment rises for ever and ever. There is no rest day or night” (Revelation 14:11). They will be forever denied the rest promised to the saints.
It says the smoke rises forever. In Isaiah 34:10 Edom, a place on Earth, is said to be burning forever and that it has smoke rising forever, but it’s not still burning and smoking. This is called apocalyptic language and it’s meant to be dramatic, not literal in this case.
“No rest day or night” does not presuppose eternity. Literally that means for one day and one night they won’t rest. There is pain involved in the second death, but it isn’t eternal.
None of these passages indicates any promise of rehabilitation or restoration once the final judgment is pronounced. No sanctifying agent is revealed in connection with the lake of fire or Gehenna. The fire is parallel to the “worm” of Mark 9:44,46,48 (KJV). It is looked at as punitive, not purifying. There will be no second chance. This should stir the Church to proclaim the message, “Now is the day of salvation” (2 Corinthians 6:2).