In that day the remnant of Israel and the survivors of the house of Jacob will no more lean on him who struck them, but will lean on the LORD, the Holy One of Israel, in truth. A remnant will return, the remnant of Jacob, to the mighty God. For though your people Israel be as the sand of the sea, only a remnant of them will return. (Isaiah 10:20–22 ESV)
Isaiah declares a remnant will come about in the future. Verses 21-22 drives home this truth to the hearers. “A remnant will return” is the name of the son of Isaiah, Shear-Jashub (cf. Isaiah 7:3). Isaiah declares that not all of Israel that will be delivered. Notice verse 22, “For though your people Israel be as the sand of the sea, only a remnant of them will return.” This is a direct reference to the Abrahamic promise. Recall that when God made a covenant with Abraham that through his offspring all the nations of the earth would be blessed, declaring that he would multiply Abraham’s offspring like the stars of heaven and the sand of the sea (cf. Genesis 22:17). God is recalling his covenant promise by not destroying the nation. It will not be the complete end of the nation of Israel. But only a remnant will return to the mighty God.
Verse 20 tells us that the remnant will be those who no longer depend on outsiders, but will faithfully depend on the Lord alone. This dependence is a picture of weakness resting on strength. They will not simply say that they rely on the Lord. They will truly rely on the Lord. They will not say the words, but will faithfully depend on God. This is a picture of what it means to return to the mighty God (10:21). The truthfulness of the nation’s faith will be demonstrated by their action of choosing to trust the Holy One of Israel, the Mighty God, rather than someone else or something else. So Isaiah states an important truth: the Abrahamic promises are not an absolute guarantee of blessing for people who fail to trust God.
The apostle Paul quotes this passage from Isaiah in Romans 9:27 and makes the same application.
And Isaiah cries out concerning Israel: “Though the number of the sons of Israel be as the sand of the sea, only a remnant of them will be saved, for the Lord will carry out his sentence upon the earth fully and without delay.” And as Isaiah predicted, “If the Lord of hosts had not left us offspring, we would have been like Sodom and become like Gomorrah.” (Romans 9:27–29 ESV)
In Romans 9:6 Paul declared that the word of God has not failed. Not all who are descended from Israel are truly Israel. Paul spends the ninth chapter of Romans proving this point. Not all the sons of Abraham were part of the covenant blessing (Isaac was, not Ishmael, nor the other sons of Abraham from Keturah; cf. Romans 9:7-9). Further, not all the sons of Isaac were part of the covenant promise (Jacob was, not Esau; cf. Romans 9:10-12). In Romans 9:27-29 Paul quotes Isaiah to prove his point. Though the number of Israel is great, only a remnant will find salvation. The true people of God, Israel, are known by their faith in the mighty God, not by ethnicity. The whole nation would not be saved. In fact, God is showing that it has always been that a remnant would receive salvation, though many could call themselves children of Abraham. Only those who were faithfully depending on the Lord would be found to be God’s people, the remnant, the true children of Abraham according to the promise.
I think we have the right to make the same application today. Not all “Christians” are Christians. Just because you were baptized does not mean that you are part of God’s faithful remnant. Just because you accepted Jesus and confessed him as the Son of God does not mean you are part of his glorious kingdom. The remnant are those who go past the external acts of obedience (while obeying those commands, of course) and faithfully put their hope and reliance on God. The remnant is a group of people who obey the Lord because they are faithfully relying on God, not by merely accomplishing some list of acts. The saved of God are those who do merely claim to be a follower of Jesus, but from the heart seek the will of God and desire to obey all that he has commanded in his holy word, the scriptures. God wants people who depend on him alone, and nothing else. They will receive the promises of God.