In Chicago, I knew lots of people who escaped from Communist Poland. None of them became disillusioned because life in the West, no matter how hard it was, was much better than it was back home. None of them ever caused any problems, or had a desire to return to Communism.
Instead of mass emigration stopping, we would see more chain migration as once a critical mass of immigrants is reached, those immigrant communities are able to provide more support structure for family members, friends, and old neighbors.
Of course, in actuality, the West would only want to accept so many millions of immigrants and then want to clamp things down. Of course, by then, the entire Communist experiment is discredited and their rule has collapsed, so it's no big deal. Simply move the 1990s forward however many decades.