After the time of King Solomon, the Hebrew people were split into two nations. Two tribes (Judah and Benjamin) reminded under the rule of the family of David. While the other 10 tribes (under the name Israel) separated and had a series of all bad rulers not related to David.
Israel would be overthrown by the Assyrians and the people taken captive. Judah would survive (because Egypt attacked the Assyrians and made them turn back before they took Israel.) Judah would remain a nation for another 100 years.
Judah would eventual be overthrown by the Babylonians and the people taken away of captives. But after 70 years they would be freed and allowed to return to Judah. There never was a release and return for the people carried away from the other tribes.
While some if the 10 tribes would maintain their heritage and eventual return once Judah had returned, the majority remained in Assyria, merged into their culture, married in their race, and eventual disappeared as a people.
The others that returned with Judah merged with them and began to give up their separate tribal heritages. The all became part of Judah/Judea or the "Jews."
The member of the 10 tribes that returned to Judah still exist today. But they have became simply "Jews" and no longer retain their separate tribal names. Those who did not return and disappeared into the culture and gentics of the Middle East.
There is no evidence that the 10 lost tribes migrated somewhere, came to America on rafts, etc. They simply intermingled with the people around them and lost their cultural identity. (They can still be found genetically in many people from the Middle East.)