Back when the U.S.S.R was still around, Cuba had many people leaving for the more economically prosperous America. The Coast Guard had the policy that stated if you were caught out at sea you were to be deported back to Cuba, but if you made it on to American soil, with most immigrants landing in Florida, you were allowed to stay.
Please note also that this is more of a history question, as it has nothing to do with the Spanish language.
