The tribes of Judah and Benjamin with the Levites should not be considered "only"and yes there were those from the Northern Kingdom that were absorbed into Judea even possibly through intermarriage but they became identified with the Southern Kingdom. They too are of those that know that they are Israelites. There are exceptions for many reasons but I am talking generally about the identity of the Southern Kingdom and what happened to them as opposed to what happened to most of the people of the Northern Kingdom. The Old Testament is written largely around the two Kingdoms, the differences between them and that in the end they shall come gloriously back together again.
The Bible repeatedly says that many Israelites were dispersed though out the whole world. The side that is "Judah" He did not divorce and send away. Yes, they ended up being out there in the world also but they never lost their identities as "The Chosen of God". They have always looked to Jerusalem with longing in their hearts believing in the prophesies about the coming Messiah and their ultimate return to Israel (at least the faithful among them). The side that was Sameria i.e. the Northern Kingdom He dispersed though out the whole world but they on a whole lost their identities as descendants of Abraham, Israelites. I believe that many people in the world today are descendants of Abraham and are unaware of it. Many who hate Israel may even be part "Jewish" and do not know it. Abrahams descendants would be as the sands on shore and numbered as the stars. Where are all these Israelites? They are us, I believe, many of us, but we don't realize it. The LORD knows though.
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Hsa 1:4 And the LORD said unto him, Call his name Jezreel; for yet a little [while], and I will avenge the blood of Jezreel upon the house of Jehu, and will cause to cease the kingdom of the house of Israel. _______________________________
Hsa 1:6 And she conceived again, and bare a daughter. And [God] said unto him, Call her name Loruhamah: for I will no more have mercy upon the house of Israel; but I will utterly take them away. _________________________
Hsa 1:9 Then said [God], Call his name Loammi: for ye [are] not my people, and I will not be your [God].
Hsa 1:10 Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, [that] in the place where it was said unto them, Ye [are] not my people, [there] it shall be said unto them, [Ye are] the sons of the living God.
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A central theme in The Old Testament is the bringing together of the two houses of Israel that had been split up between the N. and S. Kingdoms. If, on a whole, the two Kingdoms have been as one even in the days of Jesus why would The LORD speak of them coming back together at the end of the age?
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Hsa 1:10 Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, [that] in the place where it was said unto them, Ye [are] not my people, [there] it shall be said unto them, [Ye are] the sons of the living God.
Hsa 1:11 Then shall the children of Judah and the children of Israel be gathered together, and appoint themselves one head, and they shall come up out of the land: for great [shall be] the day of Jezreel.
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2Ki 18:9 And it came to pass in the fourth year of king Hezekiah, which [was] the seventh year of Hoshea son of Elah king of Israel, [that] Shalmaneser king of Assyria came up against Samaria, and besieged it.
2Ki 18:10 And at the end of three years they took it: [even] in the sixth year of Hezekiah, that [is] the ninth year of Hoshea king of Israel, Samaria was taken.
2Ki 18:11 And the king of Assyria did carry away Israel unto Assyria, and put them in Halah and in Habor [by] the river of Gozan, and in the cities of the Medes:
2Ki 18:12 Because they obeyed not the voice of the LORD their God, but transgressed his covenant, [and] all that Moses the servant of the LORD commanded, and would not hear [them], nor do [them]. ____________________________________
Jer 3:8 And I saw, when for all the causes whereby backsliding Israel committed adultery I had put her away, and given her a bill of divorce; yet her treacherous sister Judah feared not, but went and played the harlot also.