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.
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.