Does God predestine some to be saved and some to be lost? Are there some people God will not save?
The Bible clearly teaches that believers have been called from before the foundation of the earth, so it’s not shocking to us that God has elected those whom He will save. The Apostle Paul wrote that God “chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will” (Eph 1:4-5). From before time began, God has purposed to elect some to salvation, but obviously, not everyone, so how do we reconcile the fact that God calls and saves some by His election while He rejects others who are “fitted for destruction?” Anticipating the objection that God only saves some, Paul asks, “What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory” (Rom 9:22-23). The Potter has power over the clay vessels, so He has every right to save what He wills and discard those whom He will, so it sounds like people have no choice and are helpless victims of God’s election, but there’s more to it than that. 
The Apostle Paul addresses those who reject God from the beginning. It’s not that they didn’t have a choice, because they refuse to acknowledge the obvious existence of God. For example “what can be known about God is plain to them, because God has shown it to them” (Rom1:19). This shows that they know God exists because “his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse” (Rom 1:20), so even though “they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened” (Rom 1:21). Instead of worshiping the Creator, they worship the creation itself, and because of that, “God gave them up in the lusts of their hearts to impurity, to the dishonoring of their bodies among themselves, because they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed forever! Amen” (Rom 1:24-25). When people continually reject the light that God sends them, and they choose to reject God even though they know He exists, God gives them up to their own lusts and pleasures, or gives them up to a reprobate mind; a mind devoid of judgment. They willfully rejected Christ in order to continue to live in the temporary pleasures of sin, but that’s a tragic mistake. Paul, almost as if pleading with the sinners, tells them it is “because of your hard and impenitent heart you are storing up wrath for yourself on the day of wrath when God’s righteous judgment will be revealed” (Rom 2:5).
The Bible teaches that whoever comes to Christ and puts their trust in Him will be saved. It’s not off-limits to people as we might imagine because God will move heaven and earth to save one sinner who is sincerely seeking to worship Him in spirit and in truth (John 4:24). The Bible doesn’t say we are helpless victims, locked into a Christ-less eternity, but rather, Jesus says “this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day” (John 6:40), so “everyone who lives and believes in me shall never die” (John 11:26a). When Jesus was speaking about entering the kingdom with Nicodemus, He said that “whoever believes in him should not perish but have eternal life” (John 3:16b). That “whoever” means the lady across the street; it means your co-worker; and it means that family member who’s persecuted you for your faith for all these years. By Jesus saying that “whoever believes in” Me, He is saying, people have a choice to believe in Him. We are not predestined to hell because Jesus said that “everyone who lives and believes in me shall never die,” so Jesus is asking you, “Do you believe this?” (John 11:26)? To believe is a choice, but to not believe is also a choice, even though people know God exists. The psalmist wrote, “The heavens declare the glory of God, and the sky above proclaims his handiwork. Day to day pours out speech, and night to night reveals knowledge” (Psalm 19:1-2).
Are there some people that God will not save? Yes! He will not save those who reject His Son, Jesus Christ, but everyone has a choice. People who debate about God not saving some while He saves others don’t understand that people are free to choose Christ. They can choose to believe in Christ, even though God’s Spirit must quicken them in order for them to believe (Eph 2:1-4), so why God’s predestines some while not others is something I think we all wrestle with, but instead of focusing on God only saving some, we should rejoice that God saves any. We have nothing in ourselves that motivated God to save us. It was purely out of His love that He chose us and not others, but that doesn’t mean others are not off the hook. They know God exists but they still choose to live in sin. If they are to believe in Christ, they recognize they must give up their sins, and most are not willing to do that. Of course believers are not sinless, but they know that (1 John 1:8, 10). If anyone acknowledges their sins and confesses them to God, they are cleansed (1 John 1:9) and become a new creation in Christ (2 Cor 5:17), and they receive the righteousness of Christ (2 Cor 5:21). That’s all I know for sure. I not sure how it works together where God predestines some and yet Jesus says that “whosoever may come” can believe. That’s still a mystery to me, but who can fully know the mind of God? I’m just glad He chooses to save some. What about you? “Do you believe” (John 11:26c)?
Here is some related reading for you: Why Forgiveness is More Important for you than for Others 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible: English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.