If you were living in the time of the destruction of the Northern kingdom, you would have many options where to go. Certainly many individuals went south to join the Tribes of Yehuda and Benyamin. By the time of the exile of the North, many individuals had intermarried into different tribes. Once they left the North, there was no longer any reason to keep together as a separate tribe. Sancheriv, the conqueror of the North had an interest in moving people around so they would lose solidarity and loyalty to their conquered land. He moved the 10 tribes into various places. Some of the tribes that stayed in tact were later brought back by the prophet Yirmeyahu. But eventually ALL of the 12 tribes were mixed together in exile and only Levi and Cohen people kept track of their lineage. All the tribes are "lost". So the masses of Jews all over the world are a mixture. Some groups of people with Jewish customs, like the ones in Afghanistan, are likely remnants of the original 10 tribes. Possibly also the Ethiopian Jews and some in India. There are small groups of peoples that have been found that say they go back to biblical Israel but there's no proof. The sages say that in the end of days a prophet or Elijah will be able to separate everyone's lineage, and at that time it is understood that the tribal affiliation, including the "10 Lost Tribes" will return.