Yes, indeed, but if sins don't get dealt with in judgment for those who won't believe, how is a sinless heaven preserved?
That's a different question than the first. All sin is dealt with in judgment. Unbelievers (finally impenitent) will be destroyed completely (by fire).
Mal_4:3 And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the LORD of hosts.
Eze_28:19 All they that know thee among the people shall be astonished at thee: thou shalt be a terror, and never shalt thou be any more.
Consider:
All darkness [shall be] hid in his secret places: a fire not blown shall consume him; it shall go ill with him that is left in his tabernacle. (Job 20:26)
This [is] the portion of a wicked man from God, and the heritage appointed unto him by God. (Job 20:29)
For what portion of God [is there] from above? and [what] inheritance of the Almighty from on high? (Job 31:2)
[Is] not destruction to the wicked? and a strange [punishment] to the workers of iniquity? (Job 31:3)
The wicked shall be turned into hell, [and] all the nations that forget God. (Psalms 9:17)
Oh let the wickedness of the wicked come to an end; but establish the just: for the righteous God trieth the hearts and reins. (Psalms 7:9)
Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest: [this shall be] the portion of their cup. (Psalms 11:6)
Thou shalt make them as a fiery oven in the time of thine anger: the LORD shall swallow them up in his wrath, and the fire shall devour them. (Psalms 21:9)
For yet a little while, and the wicked [shall] not [be]: yea, thou shalt diligently consider his place, and it [shall] not [be]. (Psalms 37:10)
But the wicked shall perish, and the enemies of the LORD [shall be] as the fat of lambs: they shall consume; into smoke shall they consume away. (Psalms 37:20)
For the LORD loveth judgment, and forsaketh not his saints; they are preserved for ever: but the seed of the wicked shall be cut off. (Psalms 37:28)
But the transgressors shall be destroyed together: the end of the wicked shall be cut off. (Psalms 37:38)
As smoke is driven away, [so] drive [them] away: as wax melteth before the fire, [so] let the wicked perish at the presence of God. (Psalms 68:2)
Let them be blotted out of the book of the living, and not be written with the righteous. (Psalms 69:28)
For in the hand of the LORD [there is] a cup, and the wine is red; it is full of mixture; and he poureth out of the same: but the dregs thereof, all the wicked of the earth shall wring [them] out, [and] drink [them]. (Psalms 75:8)
All the horns of the wicked also will I cut off; [but] the horns of the righteous shall be exalted. (Psalms 75:10)
When the wicked spring as the grass, and when all the workers of iniquity do flourish; [it is] that they shall be destroyed for ever: (Psalms 92:7)
For, lo, thine enemies, O LORD, for, lo, thine enemies shall perish; all the workers of iniquity shall be scattered. (Psalms 92:9)
Let the sinners be consumed out of the earth, and let the wicked be no more. Bless thou the LORD, O my soul. Praise ye the LORD. (Psalms 104:35)
And a fire was kindled in their company; the flame burned up the wicked. (Psalms 106:18)
The wicked shall see [it], and be grieved; he shall gnash with his teeth, and melt away: the desire of the wicked shall perish. (Psalms 112:10)
The LORD preserveth all them that love him: but all the wicked will he destroy. (Psalms 145:20)
But the wicked shall be cut off from the earth, and the transgressors shall be rooted out of it. (Proverbs 2:22)
As the whirlwind passeth, so [is] the wicked no [more]: but the righteous [is] an everlasting foundation. (Proverbs 10:25)
The hope of the righteous [shall be] gladness: but the expectation of the wicked shall perish. (Proverbs 10:28)
The righteous shall never be removed: but the wicked shall not inhabit the earth. (Proverbs 10:30)
The wicked are overthrown, and [are] not: but the house of the righteous shall stand. (Proverbs 12:7)
The light of the righteous rejoiceth: but the lamp of the wicked shall be put out. (Proverbs 13:9)
The house of the wicked shall be overthrown: but the tabernacle of the upright shall flourish. (Proverbs 14:11)
For there shall be no reward to the evil [man]; the candle of the wicked shall be put out. (Proverbs 24:20)
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. (Ezekiel 18:4)
The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him. (Ezekiel 18:20)
Behold, the day of the LORD cometh, cruel both with wrath and fierce anger, to lay the land desolate: and he shall destroy the sinners thereof out of it. (Isaiah 13:9)
They that sanctify themselves, and purify themselves in the gardens behind one [tree] in the midst, eating swine's flesh, and the abomination, and the mouse, shall be consumed together, saith the LORD. (Isaiah 66:17)
And they shall go forth, and look upon the carcases of the men that have transgressed against me: for their worm shall not die, neither shall their fire be quenched; and they shall be an abhorring unto all flesh. (Isaiah 66:24)
For while [they be] folden together [as] thorns, and while they are drunken [as] drunkards, they shall be devoured as stubble fully dry. (Nahum 1:10)
For as ye have drunk upon my holy mountain, [so] shall all the heathen drink continually, yea, they shall drink, and they shall swallow down, and they shall be as though they had not been. (Obadiah 1:16)
I will utterly consume all [things] from off the land, saith the LORD. (Zephaniah 1:2)
I will consume man and beast; I will consume the fowls of the heaven, and the fishes of the sea, and the stumblingblocks with the wicked; and I will cut off man from off the land, saith the LORD. (Zephaniah 1:3)
Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death. (James 1:15)
And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell. (Matthew 10:28)
For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (John 3:16)
For the wages of sin [is] death; but the gift of God [is] eternal life through Jesus Christ our Lord. (Romans 6:23)
But that which beareth thorns and briers [is] rejected, and [is] nigh unto cursing; whose end [is] to be burned. (Hebrews 6:8)
But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up. (2 Peter 3:10)
And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them. (Revelation 20:9)