What is the sound opinion about eternity in Hell? If there is no eternity in Hell, then where shall its dwellers go if they are not allowed to enter Paradise, according to the Saheeh narrations, and at the same time will not die because death would vanish?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

As a matter of fact, two types of people will enter Hell: the first type is represented by believing monotheists who sometimes followed their whims and committed sins. Thus, their evil deeds will come to exceed their good deeds. They will enter Hell and will stay there as long as Allaah Wills, then they will be brought out of Hell and be permitted into Paradise by the Grace of Allaah. On the other hand, the second type is represented by non-Muslims who die insisting on their disbelief. They will remain in Hell forever and ever and whenever their skins are thoroughly burnt, Allaah shall replace them with fresh skins so as to taste the Torment of Hell. Added to this, they will never die, nor will they be relieved of the torment.

Actually, there are many texts from the Quran and Sunnah that suggest this meaning explicitly and cannot thus be interpreted otherwise. This meaning is expressed throughout the Quran. You may read Chapter Al-Bayyinah (Chapter 98 of the Quran), if you wish, as an example of this.

Allaah Knows best.