The house of Jacob refers to the persons and families who have descended from Jacob. With this phrase confirmation is given that the political existence of Israel as represented by the house of Jeroboam (the sinful kingdom) would come to an end, but some individuals (a remnant) descended from Jacob would survive.1
8 Behold, the eyes of the Lord GOD are upon the sinful kingdom, and I will destroy it from the surface of the ground, except that I will not utterly destroy the house of Jacob,”declares the LORD.