Lk 12:5 But I will show you whom you should fear: Fear him who, after the killing of the body, has power to throw you into hell. Yes, I tell you, fear him.
It is hell to be apart from God, whether only in spirit after the physical body dies, or whether it is the lake of fire, where the spirit with the new, resurrected body, the spiritual body goes.
Punishment is in the lake of fire. Punishment is not disappearing forever.
John 17:5 "Then they will go away to eternal punishment, but the righteous to eternal life."
Mark 9:48 where "'the worms that eat them do not die, and the fire is not quenched.'
Did you read that? In Mark, we are told the fire is not quenched, surely, the fire is the punishment, and disappearing forever is not.