The thief on the cross was a follower of Barabbas. Barabbas was a thief in the hills around Jerusalem. There were a number of these fellows with their bands of followers. What is interesting is that some of these leaders claimed to be the expected Messiah, and some of their followers believed them to be just that. With that in mind, IF the thief on the cross had been looking for the Messiah and suddenly realized he had followed the wrong one, then you don't have a 'last minute conversion' in the sense that is being talked about here, but you have a searcher who finally found what he was searching for at the last minute.
I have a feeling that many 'last minute' or deathbed conversions run along this line. My dad's did. He had been searching for the truth his whole life and taught us to do the same. But it was not until he was dying -- about a couple of months before -- that he asked me, finally, about my faith. I told him my story. He patted me on the knee and said, "Well, you're one kid I won't have to worry about."
He got sicker and sicker. Sometime during that last two months of his life, the Lord showed Dad that HE is the way, the truth and the life. My Dad fully embraced that and died full of joy.
But I have serious reservations that a person who has been preferring the lie his or her whole life is going to make a last minute switch. They get hardened, the Bible tells us....
There are some dearly loved and departed relatives I pray were not too hardened before death, but I come from a long line of non-Christians, and I am only one of two in my generation of siblings and cousins, I think, who has become a follower of Christ.
But if a person truly has wanted to know the truth and kept searching for it and following what he knows of it, the the Father will lead that person to Christ, and Christ will not turn him or her away -- no matter what time of life the conversion comes.