Are the names of the Destroyer and his constantly sinning demon companions written in the God's Book of Life? Of course not. Revelation 20:10 affirms this: “The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet are [were cast]. And they will be tormented day and night forever and ever.” The Scriptures reveal that it is impossible for God to lie (Hebrews 6:18). Yes, Satan and his demons are to be burned up in the Lake of Fire prepared for them, as Jesus states in Matthew 25:41. According to God's law, death is what they have earned for their sins.
We should understand that, biblically, forever does not always means “everlasting.” It sometimes indicates “as long as conditions exist.” For instance, the Old Covenant sacrifices were instituted forever. The book of Hebrews, however, shows that they are clearly no longer required for the sons of God. “Forever” lasted only until Christ died for our sins. Ezekiel 44 suggests that they will be revived in the future for a brief time, but when the Lake of Fire occurs, they will no longer be needed for a relationship with God (II Peter 3:10).
II Peter 3:13 makes an encouraging statement immediately following Peter's statements about the Lake of Fire: “Nevertheless we, according to His promise, look for new heavens and a new earth in which righteousness dwells.” A dwelling is where a person or family lives. In the New Heaven and New Earth, only righteousness dwells in them.
Does this mean “except for the unrepentant demons who continue living on despite the Lake of Fire because God cannot exterminate their existence because He mistakenly created them of imperishable spirit”? No! They are not there because they were burned up in the everlasting fire. Not one iota of sin—not even the remembrance of sin!—will exist in those living where only righteousness dwells. The unrepentant demons will be completely purged from the New Heaven and New Earth, and only holiness will remain. By the way, “new” in II Peter 3:13 and in Revelation 21:1 is kainos, the same word Paul uses in II Corinthians 5:17, meaning “something that did not exist before.” Since there will be no unrighteousness in any form in the world to come, Satan and his fellow demon spirits must be totally annihilated.