I believe it was the Pre-Christian Jewish belief. Annihilationism is directly related to the doctrine of Christian conditionalism, the idea that a human soul is not immortal unless it is given eternal life. Salvation was a response to Jewish annihilationism.
Enoch seems to support both opinions annihilationism and eternal damnation.
" 1 Enoch 38:1, 5-6 : “When the congregation of the righteous shall appear, sinners shall be judged for their sins, they shall be driven from the face of the earth…. At that moment, kings and rulers shall perish, they shall be delivered into the hands of the righteous and holy ones, and from thenceforth no one shall be able to induce the Lord of the Spirits to show them mercy, for their life is annihilated.” Similarly, 1 Enoch 91:14 speaks of the wicked being “written off for eternal destruction.”
Jewish writer called Pseudo-Philo (70-100 CE?) argues that the wicked dead will waste away in the underworld until the final judgment, where they will be annihilated forever: “And their dwelling place will be in darkness and the place of destruction; and they will not die but melt away until I remember the world and renew the earth. And then they will die and not live, and their life will be taken away from the number of all men” (L.A.B. 16:3 ).
In a passage that’s dated to around the end of the first century CE, the Ascension of Isaiah 4:14-18 depicts unbelievers (followers of Beliar, aka Satan) as being blasted by fire from the Lord which **“will consume all the impious, and they will become as if they had not been created.
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I think both view have gone side by side for a long time. Eternal Damnation and
annihilationism. Looks like the Hell Fire and Brimstone of Eternal Damnation just won out on the popularity front. If you were a street preacher looking for converts which doctrine would you preach. When you die you become nothing and just stop existing or (You will burn in the pits of hell forever unless you follow me and give me your money?)