I once asked a Jewish acquaintance if there were any identifiable remnants left today of the Tribe of Dan -- there is some reason to believe that they were Danuna (Egyptian name for them, the Phoenicians called them dynnm), identifiable with the Greek Danawoi, or "Danaans", who were the actual people who brought the Greek language from the steppes of Russia to the land of Hellas. Moreover, out on the steppe, they may have been the enemy people identified by the Vedic hymns as the Danawo.
If so, then these Danaans are mentioned in the Vedas, are the authors of Greek civilization and are prime actors in the Iliad and Odyssey, had their images and their names carved in the Ramessid monuments of Egypt, and came at last to the Bible as the Tribe of Dan -- certainly the most spectacularly rich patrimony of any identifiable people on earth.
The answer is "yes," but very few. It is a myth that 10 tribes disappeared completely. The Bible is pretty clear that four tribes survived largely intact (Judah, Benjamin, Levi and Shimon), and that refugees from the other tribes flooded the Kingdom of Judah after Israel got overrun. And Assyrian records make clear that they deported only about 27,000 people -- mostly the nobility and young strong men.
Over time, however, tribal identifications almost entirely got lost, and nearly everyone started identifying themselves as Jewish, thanks to Judah's size and wealth. You see a similar phenomenon today in various Jewish communities. In Brooklyn, for example, the big Sephardic Jewish community largely self-identifies as "Syrian," even though many of the people who call themselves "Syrians" actually have their roots in Egypt, Lebanon, and Iraq.
A small handful of families, however, diligently preserved oral traditions of tribal affiliations. I once knew an Iraqi Jew, for instance, who's mother's maiden name was "Dani." Her family had a tradition of being from the Tribe of Dan.
I should also add that the Ethiopian community identifies itself as the Tribe of Dan, and that some prominent Rabbis, such as Ovadia Yosef, fervently back that claim. I’m more skeptical. I think the Ethiopians have their origin almost entirely from converts, as the genetic evidence supports, albeit converts from a very, very long time ago.