IIRC most people couldn't leave Soviet Union at all and those that did were never able to travel with their full family with them.
People who really wanted to emigrate - emigrated, if they were not involved in defense and didn't deal with classified information.
I have many friends who lived abroad for years with their parents in Soviet times.
Now everyone is allowed to leave the country (if they are not under trial and didn't have access to Top Secret materials in last 5 years, in such cases they'll not get a "foreign passport"). So what? Now it's getting a little better, but I was really surprised when I got an American visa in 2006. But I got a bullet-proof invitation, already had a working Australian visa and I have visited the US before (I mean - in Soviet times). For most of the single males, age 30-35, no kids, it's really hard to get a visa to so-called "free world".