John 3:16-17 WEB
(16) For God so loved the world, that he gave his one and only Son, that whoever believes in him should not perish, but have eternal life.
(17) For God didn’t send his Son into the world to judge the world, but that the world should be saved through him.
John 12:48 WEB
(48) He who rejects me, and doesn’t receive my sayings, has one who judges him. The word that I spoke, the same will judge him in the last day.
Everyone that dies as a non-believer is still redeemed from the penalty of sin - the whole world of mankind is saved from sin by Jesus' sacrifice, and everyone will therefore be resurrected to life again. However, during Christ's 1,000 year reign - the Day of Judgement - those resurrected unbelievers, living as humans on the earth, will be living under the righteous rule of Christ, without the deceptions of Satan who will be restrained until the end of the 1,000 years, and will have full knowledge (no doubts) of Jesus and God, and God's commandments. They will be restored to human perfection, and God has allocated up to 1,000 years for their restoration - this is not the narrow difficult path that Christians follow to gain eternal life, it is a wider, easier path:
Matthew 7:13-14 WEB
(13) “Enter in by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and many are those who enter in by it.
(14) How narrow is the gate, and restricted is the way that leads to life! Few are those who find it.
(Note that the path that doesn't lead to life leads to destruction, not eternal torture in fire.)
Isaiah 35:4-10 WEB
(4) Tell those who have a fearful heart, “Be strong. Don’t be afraid. Behold, your God will come with vengeance, God’s retribution. He will come and save you.
(5) Then the eyes of the blind will be opened, and the ears of the deaf will be unstopped.
(6) Then the lame man will leap like a deer, and the tongue of the mute will sing; for waters will break out in the wilderness, and streams in the desert.
(7) The burning sand will become a pool, and the thirsty ground springs of water. Grass with reeds and rushes will be in the habitation of jackals, where they lay.
(8) A highway will be there, a road, and it will be called The Holy Way. The unclean shall not pass over it, but it will be for those who walk in the Way. Wicked fools will not go there.
(9) No lion will be there, nor will any ravenous animal go up on it. They will not be found there; but the redeemed will walk there.
(10) Then Yahweh’s ransomed ones will return, and come with singing to Zion; and everlasting joy will be on their heads. They will obtain gladness and joy, and sorrow and sighing will flee away.”
Everyone that will have their names written in the book of life, i.e. will have been judged at the end of the 1,000 years reign of Christ to be worthy of eternal life, will be believers. The same words of Jesus and God will apply and be used to judge them as they are to judge Christians (whose trial is this present life, not the life after resurrection). Only those that believe in Jesus will not perish and will have eternal life, whether they take the narrow, more difficult path and become Christians, or whether they become believers after they are resurrected.
I never wrote "cease to exist", I just quoted verses that say that the second death is destruction. But you are right! For example, Satan is going to destroyed (death):
Hebrews 2:14 KJV
(14) Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil;
And God tells us in Ezekiel that this means that he will no longer exist - Ezekiel 28:13-19 (WEB):
(13) You were in Eden, the garden of God. Every precious stone adorned you: ruby, topaz, emerald, chrysolite, onyx, jasper, sapphire, turquoise, and beryl. Gold work of tambourines and of pipes was in you. They were prepared in the day that you were created.
(14) You were the anointed cherub who covers. Then I set you up on the holy mountain of God. You have walked up and down in the middle of the stones of fire.
(15) You were perfect in your ways from the day that you were created, until unrighteousness was found in you.
(16) By the abundance of your commerce, your insides were filled with violence, and you have sinned. Therefore I have cast you as profane out of God’s mountain. I have destroyed you, covering cherub, from the middle of the stones of fire.
(17) Your heart was lifted up because of your beauty. You have corrupted your wisdom by reason of your splendor. I have cast you to the ground. I have laid you before kings, that they may see you.
(18) By the multitude of your iniquities, in the unrighteousness of your commerce, you have profaned your sanctuaries. Therefore I have brought out a fire from the middle of you. It has devoured you. I have turned you to ashes on the earth in the sight of all those who see you.
(19) All those who know you among the peoples will be astonished at you. You have become a terror, and you will exist no more.”’”
I was paying attention. You have not mentioned Matthew 7 before in this thread. I've quoted Matthew 7:14 above and explained that although comparatively few people become true Christians (although it's still a lot of people!), nevertheless God's plan provides a way for non-Christians to still become believers and gain eternal life during Christ's 1,000 year reign on the earth. Many will fail to gain eternal life, for Revelation 20:7-8 tell us that after Satan is released after the 1,000 years that he will deceive many people, "the number of whom is as the sand of the sea" - an expression which means they can't be counted because there are so many. What the actual number will be we can only speculate.