I believe there is confusion in the terms used, hell is not eternal since it was created, it had a beginning. only Allah is eternal, the actual term to use would be endless.
And yes, it is recorded that death shall be slaughtered and from thereon, no more death.
(32) Narrated Ibn 'Umar: Allah's Apostle said, "When the People OF Paradise have entered Paradise and the people of the Fire have entered the Fire, death will be brought and will be placed between the Fire and Paradise, and then it will be slaughtered, and an announcement will be made,
'O People OF Paradise, no more death !
O people of the Fire, no more death ! '
So the People OF Paradise will have happiness added to their previous happiness, and the people of the Fire will have sorrow added to their previous sorrow."
(Sahih Bukhari Book #76
, Hadith #556