The real question is CAN they leave? They can't go anywhere unless they are citizens of somewhere else or have an immigrant visa for where they want to go - and normally countries won't give you an immigrant visa unless you have a skill they want or need. You can't just decide to move to another country. Certainly not the USA, which is forever complaining about illegal immigrants. I certainly can't go there except as a tourist unless an employer will sponsor me for the visa or I marry an American.
Now there's another thing... the UK, for example, has cracked down heavily on "marriages of convenience" so just having a marriage certificate isn't enough to get you a visa on the grounds of being in a relationship with a Brit. It wants to see evidence of a real relationship. Just something I happen to know about because I live in the same London borough as most of Heathrow Airport, so our civic centre's register office (which conducts civil weddings) is very familiar with spotting the signs. It's usually Indians who managed to con the Home Office with fake paperwork so they get a visa, then the registrars get twitchy about the fact that the couple don't seem to know each other well, they call the police, the police interview each of the two separately, establish that they hardly know anything about each other, and the non-Brit gets a free trip back to Heathrow for deportation. They also go on the list as not being allowed to enter the UK again for another 10 years, or maybe permanently.
Another popular method used to be getting a student visa and then not going home afterwards. The Home Office's response to that is total refusal unless you have a place in a college or university on their approved list, so if you want to study in the UK, you get your confirmed place and THEN apply for the visa. Which the Home Office will give you pretty fast knowing that you probably don't have much time before the course starts. I used to work in further education funding and we got an application for money from a "college" called "Gateway2uk". I mean, come on, who are you fooling? Of course we said no.
(Just out of interest, Heathrow keeps our local magistrates' court busy - all the drug smugglers end up there.)
This is why, when the UK had to give Hong Kong back in 1997 after the lease expired, what it did was create a new category of citizenship, British National (Overseas) in 1985. This did not give them the right to live in the UK but it made it easier to enter the UK and work towards becoming full British citizens. Parliament didn't want to make it any easier because there were over 3 million eligible Hong Kongers. But the opportunity was there and eligible Hong Kongers had 12 years to decide what to do.
And many even then thought of other places to go. Canada was popular. Go and visit Vancouver and see all the Chinese faces. Especially in Queen Elizabeth Park when there's a tai chi session going on (I have a photo of this!)
So the UK did all it was willing to do at the time. But now Hong Kong is definitely Chinese, it can't interfere any more. If anyone wants to leave, they can, but they need the money or the skills, just like anyone moving anywhere.