"In that day the remnant of Israel, the survivors of the house of Jacob, will no longer rely on him who struck them down but will truly rely on the Lord, the Holy One of Israel. A remnant will return, a remnant of Jacob will return to the Mighty God. Though your people, O Israel, be like the sand by the sea, only a remnant will return. Destruction has been decreed, overwhelming and righteous." NIV translation
God's correction will be heeded by some of the Israelites. They will repent and turn back to their Provider. Throughout the Bible, the number four is associated with trials and testing and here the word "remnant" is repeated four times. This tells of the fact that through this massive trial (the exile of God's people to Assyria) only a portion of the people will come to their senses.
For those that do not, their relationship with their Creator is destroyed in the judgment. The same is true for us today as God has called us to turn from our ways to His ways (repent) and those that do not will be judged. This same type of correction is also what is coming in the future as described in Revelation 6 and we see that the leaders of the earth will know that it is God who is really in charge.