The people of Hell will abide therein forever
Question

Will the torment of the people of Hell in Hell be neverending, or will there come a time when it will end?.
Praise be to Allah.The people of Hell will remain in Hell being tormented without end. This is indicated by a great deal of evidence from the Quran and Sunnah. 
Shaykh Ibn ‘Uthaymeen was asked: Is Hell eternal or will it come to an end? 
He replied: 
What is definite is that it is eternal, and no other view is known among the salaf. Hence the scholars made this one of their tenets of faith, so that we believe that Hell is eternal and will last forever. This is a matter concerning which there is no doubt, because Allah has mentioned the eternal nature of Hell in three places in the Quran: 
1 – In Soorat al-Nisa, where He says (interpretation of the meaning): 
“Verily, those who disbelieve and did wrong [by concealing the truth about Prophet Muhammad and his message of true Islamic Monotheism written in the Tawraatt (Torah) and the Injeel (Gospel) with them]; Allah will not forgive them, nor will He guide them to any way.
Except the way of Hell, to dwell therein forever”
[al-Nisa’ 4:168-169]
2 – In Soorat al-Ahzaab, where He says (interpretation of the meaning): 
“Verily, Allah has cursed the disbelievers, and has prepared for them a flaming Fire (Hell)
Wherein they will abide for ever”
[al-Ahzaab 33:64] 
3 – In Soorat al-Jinn, where He says (interpretation of the meaning): 
“and whosoever disobeys Allah and His Messenger, then verily, for him is the fire of Hell, he shall dwell therein forever”
[al-Jinn 72:23] 
If Allah had mentioned the eternal nature of Hell in one place, that would have been sufficient, so how about if He has mentioned it in three places? It is strange that a group of scholars are of the view that Hell will cease to exist, based on false arguments which go against what is indicated by the Quran and Sunnah, and they misinterpreted the meanings of the Quran and Sunnah and said that the words “dwell therein forever” mean for as long as it exists. 
How can this be correct? If they are to dwell therein forever, that means that Hell itself must last forever, as they will be in it. If a person is to dwell in some place forever, then the place where he will be must last forever as well, because if that place will cease to exist then he cannot dwell forever. The verse is very clear, and the arguments which go against the text are to be rejected. 
This difference of opinion which was narrated from a few scholars is to be rejected, because it goes against the clear text which every believer must believe in. Whoever goes against it because of some argument that he comes up with may be excused before Allah. But whoever studies the texts of the Quran and Sunnah will know that the view that Hell will last forever is the truth which cannot be ignored. 
Majmoo’ Fataawa Ibn ‘Uthaymeen, 2/55-56 
It says in Fataawa al-Lajnah al-Daa’imah: 
There is a great deal of evidence in the Quran and Sunnah to show that Hell will never cease to exist, and that the kaafireen will abide in Hell forever and will never come out of it. Allah says (interpretation of the meaning): 
“This, because you took the Revelations of Allah (this Quran) in mockery, and the life of the world deceived you. So this Day, they shall not be taken out from there (Hell), nor shall they be returned to the worldly life (so that they repent to Allah, and beg His Pardon for their sins)”
[al-Jaathiyah 45:35] 
“Surely, those who disbelieved in Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.), We shall burn them in Fire. As often as their skins are roasted through, We shall change them for other skins that they may taste the punishment”
[al-Nisa’ 4:56] 
“but he whom He sends astray, for such you will find no Awliyaa’ (helpers and protectors) besides Him, and We shall gather them together on the Day of Resurrection on their faces, blind, dumb and deaf; their abode will be Hell; whenever it abates, We shall increase for them the fierceness of the Fire.
That is their recompense, because they denied Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) and said: “When we are bones and fragments, shall we really be raised up as a new creation?”
[al-Isra’ 17:97] 
“But those who disbelieved (in the Oneness of Allah – Islamic Monotheism) and denied Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.), they will be the dwellers of the Fire, to dwell therein forever. And worst indeed is that destination”
[al-Taghaabun 64:10] 
“and whosoever disobeys Allah and His Messenger, then verily, for him is the fire of Hell, he shall dwell therein forever”
[al-Jinn 72:23] 
“Verily, the Mujrimoon (criminals, sinners, disbelievers) will be in the torment of Hell to abide therein forever.
(The torment) will not be lightened for them, and they will be plunged into destruction with deep regrets, sorrows and in despair therein.
We wronged them not, but they were the Zaalimoon (polytheists, wrongdoers).
And they will cry: ‘O Malik (Keeper of Hell)! Let your Lord make an end of us.” He will say: “Verily, you shall abide forever.’
Indeed We have brought the truth (Muhammad with the Quran) to you, but most of you have a hatred for the truth”
[al-Zukhruf 43:74-78] 
“And of mankind are some who take (for worship) others besides Allah as rivals (to Allah). They love them as they love Allah. But those who believe, love Allah more (than anything else). If only, those who do wrong could see, when they will see the torment, that all power belongs to Allah and that Allah is Severe in punishment.
When those who were followed disown (declare themselves innocent of) those who followed (them), and they see the torment, then all their relations will be cut off from them.
And those who followed will say: ‘If only we had one more chance to return (to the worldly life), we would disown (declare ourselves as innocent from) them as they have disowned (declared themselves as innocent from) us.’ Thus Allah will show them their deeds as regrets for them. And they will never get out of the Fire”
[al-Baqarah 2:165-167] 
“Verily, those who belie Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) and treat them with arrogance, for them the gates of heaven will not be opened, and they will not enter Paradise until the camel goes through the eye of the needle (which is impossible). Thus do We recompense the Mujrimûn (criminals, polytheists, sinners).
Theirs will be a bed of Hell (Fire), and over them coverings (of Hell-fire). Thus do We recompense the Zaalimoon (polytheists and wrongdoers)”
[al-A’raaf 7:40-41] 
“But those who disbelieve (in the Oneness of Allah — Islamic Monotheism), for them will be the fire of Hell. Neither will it have a complete killing effect on them so that they die nor shall its torment be lightened for them. Thus do We requite every disbeliever!
Therein they will cry: “Our Lord! Bring us out, we shall do righteous good deeds, not (the evil deeds) that we used to do.” (Allah will reply:) “Did We not give you lives long enough, so that whosoever would receive admonition could receive it? And the warner came to you. So taste you (the evil of your deeds). For the Zaalimoon (polytheists and wrongdoers) there is no helper”
[Faatir 35:36] 
“Truly, Hell is a place of ambush —
 A dwelling place for the Taaghoon (those who transgress the boundary limits set by Allah, like polytheists, disbelievers in the Oneness of Allah, hypocrites, sinners, criminals),
They will abide therein for ages.
Nothing cool shall they taste therein, nor any drink.
Except boiling water, and dirty wound discharges —
An exact recompense (according to their evil crimes).
For verily, they used not to look for a reckoning.
But they belied Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, and that which Our Prophet brought) completely.
And all things We have recorded in a Book.
So taste you (the results of your evil actions). No increase shall We give you, except in torment”
[al-Naba’ 78:21-30] 
And there are other verses which all indicate that the kuffaar will abide in Hell for eternity and will never come out, and it will never cease to exist. When taken all together this view is very strong and there is no room for misinterpretation .