Concerning the fate of the lost: Punishment does not mean the same as punishing. If one is burned up and ceases to be, the punishment is eternal. If the burning was to go on for that individual forever, would it not be called “eternal punishing? The death penalty is different from life imprisonment with no parole. It has been said that Adam was created with eternal life but lost it for all of us. Since then, all humans are born with a body and soul but have to believe (born again) in order to receive eternal life. How then can the unsaved then live forever?
Remember that physical death and spiritual death are different. Physical death is when the body ceases to function, but spiritual death is eternal separation from God, because our spirits are immortal. Therefore, even when a person is physically dead his or her spirit is still very much alive.
The first mention of two resurrections in the Bible is in Daniel 12:2 which says some will be resurrected to everlasting life while others will be resurrected to shame and everlasting contempt. The Hebrew word for everlasting is the same for the living as for those who suffer contempt. It means eternal, perpetual, or forever.
And in a New Testament parallel, Jesus said believing tribulation survivors will receive eternal life, while their unbelieving counterparts will receive eternal punishment (Matt. 25:46). Again, the same Greek word for “eternal” is used in both cases. It means means “without end, never to cease, everlasting.”
These two examples confirm that if believers will receive life without end, then unbelievers will receive punishment without end.
So the second death is being punished forever. Isaiah 66:24 says “their worm will not die, nor will their fire be quenched, and they will be loathsome to all mankind.” They won’t cease to exist and the fire will never go out.