They will "simply cease to exist"? This, to me, makes no sense whatsoever and has no basis in scripture. To begin with, why would God even bother resurrecting them at all if He's going to turn right around and cause them to cease to exist? If He never bothered to resurrect them in the first place, wouldn't the end effect be the same? There has got to be some logical reason why He'd resurrect them and then do away with them.
But it does have a basis in scripture. In fact, it's exactly what scripture says will happen. There is a judgment day which lasts through the thousand year reign of Jesus Christ when people will be judged for the deeds they do during that reign, this happens after the resurrection of the righteous and the unrighteous. People will not be judged for the sins they committed before they died because their death paid for those sins, but they will be judged for what they do during the thousand years Jesus rules over the earth. For Christians, the death of Christ paid for all sins (past, present and future) and they are saved from the second death and part of the first Resurrection.
Romans 3:23
For everyone has sinned; we all fall short of God’s glorious standard.
Romans 6:23
For
the wages of sin is death, but the free gift of God is eternal life through Christ Jesus our Lord.
Daniel 12:2
Many of those whose bodies lie dead and buried will rise up,
some to everlasting life and some to shame and everlasting disgrace.
John 5:28-29
28 Don’t be so surprised! Indeed, the time is coming when all the dead in their graves will hear the voice of God’s Son, 29 and they will rise again.
Those who have done good will rise to experience eternal life, and those who have continued in evil (foul practicing) will rise to experience judgment.
Revelation 20:4-6
4 Then I saw thrones, and the people sitting on them had been given the authority to judge. And I saw the souls of those who had been beheaded for their testimony about Jesus and for proclaiming the word of God. They had not worshiped the beast or his statue, nor accepted his mark on their foreheads or their hands.
They all came to life again, and they reigned with Christ for a thousand years. 5 This is the first resurrection. (The rest of the dead did not come back to life until the thousand years had ended.) 6 Blessed and holy are those who share in the first resurrection. For them the second death holds no power, but they will be priests of God and of Christ and will reign with him a thousand years.
Revelation 20:7-8
7 When the thousand years come to an end,
Satan will be let out of his prison. 8 He will go out to deceive the nations—
Revelation 20:10
10 Then the devil, who had deceived them, was thrown into the fiery lake of burning sulfur, joining the beast and the false prophet. There they will be tormented day and night forever and ever.
Revelation 20:12-15
12 I saw the dead, both great and small, standing before God’s throne. And the books were opened, including the Book of Life.
And the dead were judged according to what they had done, as recorded in the books. 13 The sea gave up its dead, and death and the grave gave up their dead.
And all were judged according to their deeds. 14 Then death and the grave were thrown into the lake of fire.
This lake of fire is the second death. 15 And anyone whose name was not found recorded in the Book of Life was thrown into the lake of fire.
It's clear from scripture that there are only two states of existence, LIFE and DEATH. And as such, eternal death is the inverse of eternal life. There is no consciousness in death because your soul (along with your body) is destroyed upon death.
Ezekiel 18:4 (King James Version)
Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine:
the soul that sinneth, it shall die.
Matthew 10:28
Don’t be afraid of those who want to kill your body; they cannot touch your soul. Fear only God,
who can destroy both soul and body in hell (gehenna).