I think you mean the Rapture. The non believer will stay on earth, along with the Demons and the Devil himself, and then God will destroy the earth with eternal fire along with the souls and demons and Devil.
They are left here to face Tribulation ( the Wrath of God ) upon the unrighteous .
But....God in His Mercy will leave 2 Witnesses for 31/2 years and some will come to be saved during the Tribulation.