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If a person has refused God's grace all throughout life, and remained outside the Church, I think it unlikely that he will have a sudden about face at the moment before death, but I don't deny the possibility, nor the possibility of God sending St. Peter himself to baptize him.

Ah, there's the rub. I agree that if someone has refused God's grace, they will be culpable, but there's no denying that there are many who have not been offered that grace, and are invincibly ignorant. Those are the people I'm referring to when I refer to an extraordinary grace offered by God at the moment of death. I'm not discounting what Boniface said, but there needs to be some clarification for the sake of those who think the Church believes every man, woman, and child on earth who doesn't receive the sacraments is going to hell. That's just not true.