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The question of whether Lucifer’s angels are tied in chains comes first from Jude 6, which says, “And the angels kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.” Jude is using a figurative language. You can’t really tie angels with chains because they are spiritual beings with no flesh and blood like humans. This verse means that angels are in bondage because they are restricted to this planet. Also, the chains, or bonds, are everlasting in the sense that the rebellious angels cannot escape from them.
And another reference to the chains is also found in 2 Peter 2:4 that says, “For if God did not spare the angels who sinned, but cast them down to hell and delivered them into chains of darkness, to be reserved for judgment.” Here, Peter’s language is also figurative, and does not serve to identify any particular place as the abode of the fallen angels. The apostle looks to the future, when the judgment determined upon Satan and his angelic followers will finally be executed (Rev. 20:10).
At the end of the world, Satan will be thrown into the lake of fire, which will turn him into ashes and end his existence for eternity “So shall it be in the end of this world. The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; And shall cast them into a furnace of fire” (Matthew 13:40-42). This fire also will destroy all sinners. In this final showdown, not one being on God’s side will die and not one being on Satan’s side will survive.