The actual salvation that is promised, from Yahweh God, is the work of God, through the righteous life of Christ through his works and atoning sacrifice, and work of his Spirit in believers, from God's grace, according to the essential faith of salvation with which believers respond to the revelation for it given to them. As it is the work of God, it does not fail.
Passages speaking of salvation for all men are speaking of gospel salvation to be made available for any of all nationalities. And what you suggest makes no sense indeed does not make sense, with your interpretation. But Hebrews, whether from Paul or not, just like other epistles, is written to assemblies of believers, and as it is with all assemblies, there may be some there with some belief, but not that essential faith of salvation, and so it is sinful, unbelieving hearts that turn away from God, this is not said to happen with those saved according to the essential faith, that is the work of God, but all in an assembly should make sure of their convictions, so true believers can be assured, and those who are not can be aware of it and truly come to salvation rather than hardening and turning away from God's grace. And good works, though not saving any, do accompany the believers of the true essential faith.