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.
Then she is the heiress of a tradition of which I stand in special awe, even though she may not be aware of it herself. Her people are very, very special. And living in Iraq, it turns out they weren't all that terribly far from the countryside of their origins, out on the steppes north and northeast of the Caspian Sea.
Before that, of course, they were part of the Proto-Indo-European-speaking Yamnaya or Kurgan Culture, 4300 years ago, and before that, of the Sredny Stog culture which appeared on the shores of the Black Sea, somewhere around the outfall of the River Bug, 7400 years ago, or just after the Black Sea basin filled up. (They might have been living down in the basin before that, who knows?)