This is a faulty theory that unbelievers will not suffer for eternity in hell but at some point their life will cease to exist.

However, the Bible states, Satan, the beast and the false prophet will be cast into the lake of fire and tormented "day and night forever and ever" (Rev 20:10). Those who align themselves with Satan and everyone whose name is not found in the book of life, will also be thrown into the lake of fire (Rev 14:9-12, 20:15). "Then they [the unsaved] will go away to eternal punishment, but the righteous to eternal life" (Mt 25:46).  Consciousness will last forever both in heaven and hell.

See also: eternal damnation.