Judging from the upvotes, it seems like people are quite interested in my grandparents' failure to emigrate from Communist China before it was too late, so I thought I'd elaborate here with more details and for greater visibility. They were all actually supporters of the Communist Party at the beginning, and saw it as potential saviors/liberators of the Chinese people and nation. They were also treated well at the beginning - one of them (being one of few people in China with a higher education) was given a high official post, and another retained a manager position at the factory that he used to own and operate.
The latter side of the family considered moving away from China prior to the Communist victory since they would be classified as "capitalists" under the new regime, but were reassured by high level party members that they would be treated well if they stayed and helped to build the "new China". They actually did relatively ok, aside from most of their property being confiscated/nationalized early on and their living standards deteriorating steadily until they were forced to share the house that they used to own with something like 4 other families, and them being left with a single room in which to live.
The other side were more straightforward "true believers" who supported Communism at an early stage, as they were part of the educated class who generally saw it as the right side of history, something that would help China leapfrog the West in terms of both social and economic progress. My grandmother on that side even tried to run away from her family to join the revolution after graduating from the equivalent of high school. Just before the Communists took power, my grandmother changed her mind, and wanted to move away from China and even got the required visas. (I asked my father why, and he said "women's intuition" which I'm not sure is really accurate but he couldn't provide further details.) But my grandfather still believed in the cause so they stayed. After the Communist victory, there was still about a year before the borders were fully shut, but it seemed like things were moving in a good direction and disproved my grandmother's worries. My grandfather was given an important post and went around making important speeches and so on.
Unfortunately he was not very good at playing politics, as his background was in physics (although plenty of natural politicians also fared quite badly during the various "movements"). His position started attracting envy from those who thought he didn't contribute enough to the revolution to earn it. He was demoted and moved from city to city as the Party assigned him to various jobs. Finally, some kind of political dispute near the start of the Cultural Revolution led to his opponents digging up an incident in his distant past, which was then used as an excuse to persecute him in various ways, including confining him in a makeshift prison for ten years. He died shortly after the Cultural Revolution ended and he was released, just before I was born. According to my father, it was from over-eating due to finally being released from the extreme deprivation of his confinement.
BTW, I wasn't told any of this when I was still a kid living in China. My parents had of course grown quite disillusioned by Communism and the Communist Party by then, but probably didn't think it would be to my advantage to show any signs of resistance to the indoctrination and propaganda that I was being fed in school and in the mass media. So I can also testify from personal experience that if those in charge of schools and the media want to, and there's enough social pressure to not resist, it's not very hard to brainwash a child.