Our knowledge of Israel History as a whole is confined only to the Southern kingdom (i.e., Judah and Benjamin tribe), as such we believe that the tribe of Judah (including Benjamin) was only tribes taken into the Babylonian captivity and furthermore, there is also the belief that the post exilic history covered only Judah. The other ten tribes of Israel (i.e., Northern kingdom), we believe, were taken captivity by the Assyrian king and subsequently lost completely forever. Little we know about these 10 tribes taken into captivity, by the Assyrian king 136 years before the Babylonian captivity.
After the death of Solomon in BC 931 his kingdom was divided into two kingdoms, and consequently the two tribes of Judah and Benjamin along with their respective lands allotted from time of Joshua followed the son of Solomon, Rehoboam and rest of the ten tribes of Israel (also known as Northern kingdom) along with their respective lands followed Jeroboam.
The king of the Northern kingdom, Jeroboam then made two golden calves, one he set up in Bethel and the other one he set up his Dan; this he did because of the fact that he thought his kingdom would be weakened if Israel always would visit Jerusalem to worship God, but this angered God very much (I Kings 12:26-30). The Levites even abandoned their pasture lands and property and then came to Judah because Jeroboam rejected them as priests, and also those from every tribes of Israel who rejected worshipping golden calves, and who were rigid in religion came to Jerusalem (2 Chro. 11:14-16).
When Asa become king over Judah, he effected better system of religion and God also blessed him, and it was known that Ephraim, Manasseh and Simeon had came over to him and settled under his care and protection (2 Chro.15:9). Although it was called Kingdom of Judah, it appeared that every tribe out of 12 Israel tribes was in the kingdom of Asa.
In BC 722 the 10 tribes of Israel were taken into captivity by the king of Assyria, who settled them in Halah, in Gozan on the Habor River and in the town the Medes which were under his kingdom (2 Kings 17:6). The manner of Assyrian conquest and subsequent rule were very much different from Romans? massacre of Jews in AD 70 When Assyria conquered Israel, the people were taken into captive and many of them were left to remain in their land, but Assyria sent foreigner and eventually cross-cultural marriage to be prevalent. Their descendents were known as Samaritans.
Six years after the captivity of the Northern tribes (Israel), Hezekiah become a king of Judah. He cleansed the temple, he reformed religious system and observed the pass over feast in which a good number of the tribes of Aser, Manasseh and Zebulun also came. About one hundred year after Assyrian king took them (Israel people) into captivity, when king Josiah, in 622 BC made in the reformation in the religious system, the remnants of Israel who were not taken into captivity, gave offering to the Lord (2 Chro. 34:9).
What is clearly seen here is that after the fall of Northern Kingdom (ten tribes of Israel), the remnants of Israel, not taken into captivity by Assyrian, continue to settle in Palestine. Although, they did not have their own king, they attached themselves to the king of Judah. When king Nebuchadnezzar captured and took control over Jerusalem, the inhabitants of Jerusalem were not only the tribes of Judah, Benjamin and Levi but also the tribes of Israel settled and so, there was no reason that they should not be among the Babylonian captivity and who continued to live in their own land had been completely assimilated before another 100 years elapsed; they had become Samaritans.
The Israel captives in Assyria did not vanish, when the king of Babylon subdivided the king of Assyria Israel captives did not gain freedom as a consequences they rather went into possession of Babylon which was quite suitable as both the Assyrians and the Babylonians lived/inhabited the same Mesopotamian region. Israel was scattered flock of ship chased away by the lion, king of Assyria devoured him, king of Babylon, Nebuchadnezzar crush his bones (Jer. 50:17). In olden days slaves were very much required to do works, when freedom was won, there was no difference in favor of slaves, slaves were slaves, that?s all; no freedom through wars, they rather went into possession of the conqueror in that war; prophet Ezekiel, who was with the Jewish captives, ministered in the captives (Ezk. 4:4, 14:1, 20:1, etc).
When the king of Persia, Cyrus conquered, there their uncommon happening which was very much remarkable, (as God already proclaimed) - permission for the freedom of the captives were issued, and as many as 42360 had at first, their home coming, among them were people of Bethel and of Ai ? people of the places where Jeroboam?s golden calves set up, were also with them (Ezek.2:28). During the reign of Persian king, Artaxerxes, some of the people of Israel (of the erstwhile Northern kingdom) also returned to their home land (Ezra 27:7) and those who returned home had sacrificial offerings for the 12 tribes, this clearly shown that who came back from the captivity fully represented 12 tribes of Israel.
Apart from the above, I would like to mention that it is very much wrongful to believed that the escaped children of Israel from the captivity would proceed to China, the land which they knew nothing about; or else, if they had to do this, they would need to cross to Persia, India (Modern Pakistan); it would not be like traveling peacefully or not like Uncle Tom proceeded to Canada from America. It would also be unwise to take exceedingly long journey with women and children without carrying sufficient food to sustain them on their way (to China) from Mesopotamia.