Answers to Quora Questions by Yair Davidiy (11 December 2017, 23 Kislev, 5778)
The Tribes that were lost were the Tribes of Ephraim, Manasseh, Gad, Asher, Dan, Naphtali, Reuben, Simeon, Issachar, and Zebulun . The Ten Tribes had been exiled by the Assyrians 2-Kings 17:5, 1-Chronicles 5;26). All of the Ten Tribes before their exile were in the north apart from Simeon which had been far to the south and southeast. The Tribe of Simeon before the Exile was ruled over by the north and attached to it as indicated by archaeological finds from Kuntillat Ajrud in Northern Sinai. The Bible (2-Chronicles 34:6) and Midrashim also confirm that Simeon had been exiled and joined up with the northern Tribes. On the other hand, the Tribe of Levi had originally been scattered among all of the Tribes. Most of Levi however before the Exile by Assyria moved to the south due to the pagan religious changes effected by Jeroboam in the north (2-Chronicles 13:9-11). There were actually 13 tribes altogether but for its own reasons the Bible always maintains a quorum of 12 by omitting one tribes or other or by counting the two Tribes of Ephraim and Manasseh as the one tribe of Joseph. Midrashim and Biblical hints relate that refugees from the north managed to escape the Assyrians and fled to Judah.
The Kingdom of Judah thus consisted of the Tribes of Judah, Benjamin, and Levi, along with representative minorities from the other Tribes. A Midrash indicates that up to 20% of the people of Judah who returned with Ezra from Babylon were refugees from the Northern Kingdom. Nevertheless, as emphasized by Nachmanides, these were considered as nullified amongst Judah and counted as part of Judah just as those of Judah who had gone with Northern Israel are considered part of the Lost Ten Tribes. The Bible has its own terminology and the Bible considers the Northern "Israel" ("Joseph", "Ephraim") to be a separate entity apart from Judah.
"Those from the Tribes of Ephraim and Simeon from Israel that were present with Judah were they who dwelt in the Land of Judah or perhaps to some degree also those who had dwelt in their own territories adjoining Judah and had fled to Judah are referred to generally as from Israel [in 2-Chronicles 35:18]. They are not mentioned by their specific Tribes since they represented only a small portion of their tribe. These are they who returned under Ezra with the Jews from Babylon. They were not expressly mentioned by their tribes since they were attached to Judah. They all settled in the cities of Judah. There was no Redemption for the [majority of the] Ten Tribes who remained in exile." Book of Redemption (Sefer HaGeulah) pt.1.
In addition to the Ten Tribes the Assyrian King Sennacherib conquered cities in Judah. He claimed to have deported more than 200,000 people.
13 Now in the fourteenth year of king Hezekiah did Sennacherib king of Assyria come up against all the fenced cities of Judah and took them.
This exile of many from Judah along with the Ten Tribes or shortly afterwards is merely hinted at in the Bible but is spoken of in Midrash Seder Olam and other sources.