As a tree falls, so shall it lie. Ecclesiastes 11:3
From the April 2011 New Yorker Cartoons
One of the great fallacies of the non-believer is that they can put off their decision about God/Jesus/Salvation until the end. Even if the person is fortunate enough to have the time (no sudden death) to address the issue, it is VERY unlikely anything will change, since reversing direction goes against the weight of their entire life.
While it is true that there have been remarkable deathbed conversions, they are few and very far between, so much so that it is an extremely risky and unreliable strategy.
One of the most remarkable deathbed conversions I have ever read was fictional and part of the best presentation I have ever read for the truth of the Gospel. It is in the apocalyptic book Father Elijah. While this wonderful book is possibly too Roman Catholic for some readers, no one can deny the overwhelmingly powerful evangelistic effort Father Elijah makes for a dying Nazi quisling. The man was responsible for the death of his protector in Poland during WWII and Father Elijah witnesses to him in the hospital. I would recommend the book as worth it for that extended passage alone and every evangelical Christian should read it.