Micah 5:3

Therefore will he give them up, until the time that she which travaileth hath brought forth: then the remnant of his brethren shall return unto the children of Israel.

Israel would be abandoned to its enemies until the appointed time when the woman in travail would bring forth her child, and that child is the promised ruler to come out of Bethlehem. Once that birth had taken place, the remnant of his brethren would return to the children of Israel. That return was fulfilled in the faithful remnant who gathered to Christ after His coming.

The remnant are the humble Israelites who kept the faith amid national apostasy and received Christ as His followers. They are distinguished from the nation as a whole by lowliness, fidelity, and acceptance of the Messiah.

The proud, backsliding nation as a body rejected Christ when He came. Because of that rejection, the special advantages first offered to the Jewish nation passed to the Gentiles.