Matthew 13:42

37 He answered, “The one who sowed the good seed is the Son of Man. 38 The field is the world, and the good seed stands for the people of the kingdom. The weeds are the people of the evil one, 39 and the enemy who sows them is the devil. The harvest is the end of the age, and the harvesters are angels.

40 “As the weeds are pulled up and burned in the fire, so it will be at the end of the age. 41 The Son of Man will send out his angels, and they will weed out of his kingdom everything that causes sin and all who do evil. 42 They will throw them into the blazing furnace, where there will be weeping and gnashing of teeth.

I’m not a biblical scholar but my understanding was there was biblical basis for it. Especially mentioned by Jesus as he was an apocalyptic preacher. Something like this sounds like it fits the bill pretty well:

The Son of Man will send out his angels, and they will weed out of his kingdom everything that causes sin and all who do evil. They will throw them into the blazing furnace, where there will be weeping and gnashing of teeth.

Like I said though I’m not a biblical scholar. Although I’m not sure simply being denied an infinite reward is that much better really. It’s still effectively an infinite punishment for something you have no control over.