Is there a Biblical basis for believing someone can be saved after dying and going to Hell?

The question is, is there any Biblical basis for the idea that a person might be saved after he dies.

The answer, I think, is yes. That is, a Biblical case can be made for some people escaping eternal punishment after they die.

Here are some passages that might help build such a case:

1. 1 Cor. 15:21-28: This passage starts out seeming to proclaim universalism: "as in Adam all die, so in Christ shall all be made alive", but then says "each in his own turn", and seems to describe a series of events. Christ is the first to be "made alive", then "those who are his at his coming", and then some other things happen, but the end result seems to still be a good result for everyone -- God is all in all.

2. Philippians 2:9-11 says: "Therefore God exalted him [Jesus] to the highest place and gave him the name that is above every name, that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father."

Take that passage in connection with Romans 10:9-10 which says that "if you confess with your mouth ‘Jesus is Lord', you will be saved” and “it is with the mouth that you confess and are saved”. So we have one passage saying that, eventually, everyone will confess with the mouth that "Jesus is Lord", and another saying that such a confession results in salvation. Since we know that not everyone makes this confession during their lives, it might be that some people make them after they die.

3. 1 Peter 3:19 and following seems to be saying that Jesus went into Hell and "made proclamation to the imprisoned spirits", referring to people of Noah's day, who would obviously have been dead by Jesus' time. The implication seems to be that these people were given an opportunity to be saved. In another place it speaks of Jesus, upon his resurrection, "leading captivity captive", possibly interpreted as referring to his leading those imprisoned spirits out of imprisonment.

Short answer:

No, there's no Biblical reason to believe that there is any opportunity whatsoever to escape hell. There are several non-Biblical arguments, but they are not based on the teachings found in the Bible.

Longer answer:

There are several groups that believe that there is an opportunity to be "saved" after death.

The LDS Church believes that the dead are still possible to redeem, and practice baptism for the Dead, for example. From an article on their site explaining Baptisms for the Dead:

Many people have lived on the earth who never heard of the gospel of Jesus Christ and who were not baptized. Others lived without fully understanding the importance of the ordinance of baptism. Still others were baptized, but without proper authority.

Because He is a loving God, the Lord does not damn those people who, through no fault of their own, never had the opportunity for baptism. He has therefore authorized baptisms to be performed by proxy for them. A living person, often a descendant who has become a member of The Church of Jesus Christ of Latter-day Saints, is baptized in behalf of a deceased person. This work is done by Church members in temples throughout the world.

This is only possible to believe, however, if you also believe in the LDS definition of Hell as a temporary prison for some (only permanent for Satan, his followers, and the "sons of perdition".

Latter-day revelations speak of hell in at least two ways. First, it is another name for spirit prison, a temporary place in the postmortal world for those who died without a knowledge of the truth or those who were disobedient in mortality. Second, it is the permanent location of Satan and his followers and the sons of perdition, who are not redeemed by the Atonement of Jesus Christ.

Outside of the LDS Church, the idea that you can be saved after death is very rare. Some groups do believe in what's known as "Postmortem Evangelism". However, from a Biblical perspective, and one held by most Christian denominations, this is not supportable. Scripture is quite clear that our eternal fate depends entirely on what occurs in this life, and that once we die in our sins, if we do not have the forgiveness of Christ, our fate is sealed.

From The Christian Research Institute

One well-known advocate of PME, Gabriel Fackre, argues that Scripture teaches that each human’s destiny is not fixed at death. The context of several key Bible passages, however, does not support his interpretation. In fact, these passages clearly say that everyone will die and be judged (Heb.9:27) and that each person’s eternal destiny, either reward or condemnation, will be based on what was done in this life (Matt.7:21–23;13:36–43; John5:28–29). Jesus, moreover, taught that each human’s destiny is fixed at death; for example, in His story of Lazarus, who was eternally in paradise, and the rich man, who was eternally in torment (Luke16:19–31). Finally, the description of the great white throne judgment in Revelation20:11–15 unquestionably indicates that our eternal destiny is based on our earthly life. In these and other passages, physical death marks the boundary of human opportunity to be saved. Belief in PME, meanwhile, has serious negative implications for Christian evangelism and missions. The weakness of PME arguments and the total silence of Scripture regarding opportunities to hear the gospel after death, therefore, should cause Christians to reject this view.