We escaped in 1966, spent a year in Austria waiting on Visas to the USA. Part of the reason we got Visas is the JFK sponsored law - putting Commie escapees to the front of the line for Visas to the USA.
My father was a Doctor, my mother a Dentist. My father's first job when we arrived in the U.S. was as a Mexican laborer - Cutting Grass in ritzy N.Y. suburbs working for a Hungarian who escaped the '56 purge
After a while my father, who never manged to pass the Boards, possible too old, ended up working in a mental asylum in Mass. - And then, Mr. Tank guy, Dukakis and the Mass. legislature passed law - ELIMINATE Mental Asylums - much better to have people with issues on the street being homeless - makes for better political ammunition - Oh no, we have too may homeless
Politics - War with different casualties
We have a system to handle asylum seekers and refugees. The legal immigration system is separate. Interesting that your parents sought refuge in the US rather than Western Europe.