At the heart of reformed “covenant” theology embraced by traditional Presbyterian teaching is the Gospel as spelled out in the New Testament. We can debate the legitimacy of “covenant” theology of which I do not believe the Bible teaches but many Calvinist that take the Bible seriously are cleansed by the blood and thus redeemed by the cross.
So, some who are died-in-the-wood are saved since they are trusting in Jesus, (which implies repentence), some who are died-in-the-wool are not because they are trusting in dogma (which does not imply repentence).
>> some who are died-in-the-wood are saved since they are trusting in Jesus <<
Well, I’ve heard Calvinist preachers say time and again that there’s nothing a man can do to save his soul. It’s all up to God. So if these Calvinists are right, then it shouldn’t matter if somebody does or doesn’t trust Jesus. As long as he is predestined, the Unbeliever will be saved just as will the predestined Believer.
Of course, there are those who will argue that the Believer has faith precisely because he IS predestined for salvation, while the Unbeliever lacks faith precisely because he ISN’T predestined. But to me, that’s circular reasoning — not really persuasive.