In the past generations this idea of repentance (although it goes farther than that) as the first step toward salvation has permeated the Christian culture. Working ones way to salvation is the scheme of Satan. God plainly says in Scripture that it is His doing not anything to do with us. God has elected His people before the foundation of the world (Eph. 1:4) we are not sovereign so we do not know who God has chosen. Here is a passage in Isaiah that petrtains to this;
Not only that, but Rebekah’s children were conceived at the same time by our father Isaac. Yet, before the twins were born or had done anything good or bad—in order that God’s purpose in election might stand: not by works but by him who calls—she was told, “The older will serve the younger.” Just as it is written: “Jacob I loved, but Esau I hated.” What then shall we say? Is God unjust? Not at all! For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” It does not, therefore, depend on human desire or effort, but on God’s mercy. Romans 9:10-16
I not saying that repentance (change of mind) is not important. I am reminded of Isaiah when I think of his manner when he was in the presence of the Almighty in Isaiah 6:5
“Woe to me!” I cried. “I am ruined! For I am a man of unclean lips, and I live among a people of unclean lips, and my eyes have seen the King, the Lord Almighty.” He knew exactly who he was in the presence of the Lord Almighty when God reveal himself to him, unclean.
So even if we are at someone death bed who you do not think has obtained salvation you really do not know. God in the final breathe can make himself known.