Satan disappears? I never read about that. I don't think thats right. Besides Satan doesn't rule over Hell.

And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand. 2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years, 3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season. (Revelation 20:1-3)

7 And when the thousand years are expired, Satan shall be loosed out of his prison

Besides Satan doesn't rule over Hell.

The question is framed as if Satan ruled over Hell. Just like the question is is framed as "if all that jazz was real" it doesn't matter that it isn't, we are speaking as if it is.

Satan never leaves. He is locked up for 1000 years during the millennial reign. He them comes out and is eternally cast into Hell.

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; (Hebrews 2:14)

12 “Son of man, take up a lament concerning the king of Tyre and say to him: ‘This is what the Sovereign Lord says:

“‘You were the seal of perfection,

full of wisdom and perfect in beauty.

13 You were in Eden,

the garden of God;

every precious stone adorned you:

carnelian, chrysolite and emerald,

topaz, onyx and jasper,

lapis lazuli, turquoise and beryl.

Your settings and mountings were made of gold;

on the day you were created they were prepared.

14 You were anointed as a guardian cherub,

for so I ordained you.

You were on the holy mount of God;

you walked among the fiery stones.

15 You were blameless in your ways

from the day you were created

till wickedness was found in you.

16 Through your widespread trade

you were filled with violence,

and you sinned.

So I drove you in disgrace from the mount of God,

and I expelled you, guardian cherub,

from among the fiery stones.

17 Your heart became proud

on account of your beauty,

and you corrupted your wisdom

because of your splendor.

So I threw you to the earth;

I made a spectacle of you before kings.

18 By your many sins and dishonest trade

you have desecrated your sanctuaries.

So I made a fire come out from you,

and it consumed you,

and I reduced you to ashes on the ground

in the sight of all who were watching.

19 All the nations who knew you

are appalled at you;

you have come to a horrible end

and will be no more.’” (Ezekiel 28:12-19)

Here are two passages that support my claim. I don't actually believe any of this nonsense, this is just moral question presented in a way to make it more fun to answer. To be fair to you, there is a verse that supports your claim.

10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever. (Revelation 20:10)