I believe redemption is possible, albeit in a somewhat different form than known traditionally.
Humans are by their very nature extremely flawed creatures, so cultures since the dawn of time have struggled to facilitate the individual's redemption. Redemption allows the individual to not only take responsibility for past mistakes, but move forward toward a brighter future.
Traditionally, in the West, redemption was achieved by giving your life to Jesus Christ and being "washed in the blood of the lamb." The traditional redemption allowed the "sinner" to show those he or she had hurt in the past that he or she regretted his or her actions. It was a chance to have a clean break from the past in a public and immediate manner. The person was now "reborn" with "Christ in their heart."
In today's secular world, however, redemption is more difficult. It is not impossible. Rather than being "saved" the closest thing the modern secular humanist can hope for is some sort of "closure" on a difficult time in his or her life.
Such closure can come in many different forms. It can be as simple as saying "I'm sorry." The crux of closure is it marks the end of one era in an individual's life and the beginning of another. It doesn't mean the interpersonal relationships damaged through the wayward soul's actions will snap back into their original place.
It does mean, however, that the healing can begin and the poor decisions made previously may eventually be forgiven, if not forgotten.