In the early 1960's my stepfather was a fugitive in Havana, being looked for by Castro's Secret Police--with a price on his head.

Eventually, he was smuggled out of Cuba in a crate with diplomatic tags on a Mexican Airforce transport plane. The Mexicans saved his life, but they wouldn't let him stay there, he had no choice but to enter the USA illegally. He turned himself in to the US authorities after swimming across the Rio Grande, and they tried to take him back to Mexico, but the Mexicans wanted no part of him. He spent six months in a concentration camp at McCallen TX, until they were convinced he was a genuine refugee and not a spy.

They let him stay in the US as long as he was a refugee from Communism, but he'd have to go back and face a firing squad the moment relations between Cuba and the US improved. He came to Florida where there were agencies set up to give Cuban exiles support, got working papers, a job, and met and married my mother.

He wanted to be a US citizen, but he had "entered the country illegally", so he couldn't even apply. He wound up having to go to Canada, get some papers stamped at the US embassy in Ottawa, so he could enter the US "legally" and start the long process of becoming a citizen.

My cousin Rudy came in about the same time, under the Pedro Pan program, which allowed him to enter the US for school (although his parents could not follow him). To become a citizen, he had to join the Army, and only then could he sponsor his parents as a US citizen. The funny part is that after he got his citizenship, the Army realized he was a from a Communist country, and so were his parents, so he was promptly discharged as a security risk.