Many probably continued to be slaves. But instead of serving their Assyrian masters, many probably had to serve Babylonian masters, and then the Media-Persian masters.
For what it’s worth, in the summer of 07, I was hiking in the Rockies, and was passed up by a couple of young Jewish looking fellows. They were wearing the skull cap things. I asked them what tribe they were from. They said, “Ephraim”.
It was some 200 years later that King Neb took the House of Judah to Babylon. There is NO way those ten tribes went to Babylon... they headed up over the Caucasus Mountains ... hence the word caucasian.