"I don't know."
Let me both explain and qualify.
I think Scripture contains many things that are both grandly clear and sublimely ambiguous. I think the debate over libertarian free will, compatibility and determinism is one maybe that we aren't privy to. At a glance, the Old Testament seems to advance a form of openness and the New Testament counters that with much of what Paul writes, particularly in Romans(1). That does not mean we can't choose a valid option (or that they don't all have something going for them), but it does mean that I'm not convinced that Scripture all that entirely consistent in giving us one way to look at that one example. Maybe so for this doctrine of hell as well.
I don't know if everyone who isn't elect and/or chooses to reject God will be burned forever or will be eventually irreversibly destroyed. I just don't know.
Maybe the Bible doesn't want us to know, or even more dramatically, maybe God doesn't want us to know. G.K. Beale in his commentary on the Apocalypse of John seems aware of the possibility of universalism at the end of the letter being possible and he does his best to counter this. Universalist theologian Robin Parry does the same, concurring that there is indeed tension between open city gates and a lake of fire, opting for his legitimate hermeneutical bias in favor of the restoration of all things(3).
I remember a biblical scholar speaking on Origen and Universalism and to paraphrase from memory, the scholar concluded that both "Paul and Origen seemed both particularly exclusive and strongly universalistic." In other words, Origen and Paul mentioned the beauty of universal salvation in one context (specific churches e.g. Colossae) and the terrifying possibility of complete destruction in his first letter to the Thessalonians. This isn't to say I agree with the scholar, but I definitely see the tension exhibited.
Maybe God doesn't want us to know.
Knowing many of us, to know everyone will be saved could to lead to laziness. On the other hand, knowing many of us in the same way, we are very quick to use metaphorical fire to frighten "belief" into an endangered soul that ultimately leads to the possibility of apostasy or hostility towards the church. The wonderful conditionalists at ReThinking Hell have been irenic in their many conversations with me on this most difficult doctrine.
I just don't know.
I would resonate most strongly with Thomas Johnson who says,
"The case for universalism is stronger than is usually realized. God's saving love for the world is a prominent biblical theme from Genesis through Revelation. God is the Lord and Savior of all and does not want any to perish but all to be saved. God provided salvation, forgiveness, justification, and reconciliation for all, indeed for all creation. Eventually, everyone will confess Jesus Christ as Lord. Yet, we do not know how God's judgment works out with respect to individuals." (2).I suppose it boils down to faith. Faith in the power of the Spirit to bring forth salvation and that, somehow, all would eventually reach their telos. The justification for hope that "all would be saved" is indeed something many theologians of the past and present have embraced (Balthazar, Moltmann, Volf, Walls and others).
The God who saves assures us that that He is loving and just, no one escapes from his justice and that He will be "ta panta en pasin" in 1 Cor. 15:28. I tend to take solace in this, and Scot McKnight is generous to include those that are"eschatologically agnostic" into the fold of simply not being able to at this current time fix a tension seen in Sacred Scripture. There is indeed hope beyond this life. I take great comfort in that.
1). Incidentally, open theism is a budding research project for me. Consider a possible thought change on this one. Maybe?
2). T.F. Johnson, "Universal Salvation? The Current Debate" pg97. In spite of his comment, Johnson is not a universalist, instead suggesting that annihilationism is the best option based on the data.
3). Gregory MacDonald aka Robin Parry, "The Evangelical Universalist" pg133-34. This remains the best case for universalism that I have read, and I'm impressed with some of his exegesis on the Apocalypse of John.