Babylonian Exile and Babylonian Jews

What happened to the Jews who did not return from Babylonian Exile? Did they just assimilate into the dominant culture in Exile? Or did they return at a later date? And if they did not return, can we assume that some of the descendants of King David are currently living in the Modern State of Iraq, or thereabouts?

The Jews who remained in Babylon during the time of Ezra, were eventually joined by other Jews who were exiled there with the destruction of the 2nd Temple and dispersion about the year 70 CE. Babylon even became the world Torah center from about 250 CE and on. Obviously some assimilated, but many of the their descendants only returned from Iraq in the late 1940’s-early 50’s with the rise of the State of Israel. In addition, because of anti-Semitism and the moving of the world Torah center to Kirwan (North Africa, about the year 900 CE), and subsequently to Italy, Germany, Spain and East Europe, many of them moved as well. Theoretically, there are descendants of King David all over the world.