'Faithlessness' in the Bible

Then Ezra got up from before the house of God and went into the chamber of Jehohanan the son of Eliashib [and spent the night there]. He did not eat bread nor drink water, for he was mourning over the [former] exiles’ faithlessness.

“Return, O faithless sons,” [says the Lord],“I will heal your unfaithfulness.”[They answer] “Behold, we come to You,For You are the Lord our God.

“But the shameful act [of idolatry] has consumed the labor of our fathers since our youth—their flocks and their herds, their sons and their daughters.

I will heal their apostasy and faithlessness;I will love them freely,For My anger has turned away from Israel.

What then? If some did not believe or were unfaithful [to God], their lack of belief will not nullify and make invalid the faithfulness of God and His word, will it?