No, not in the United States, in Europe. According to this email from Joel Rodriguez posted on Los Miquis....
A Cuban wanting to normalize his status in Europe has three options. The first is to marry a European, which often entails marrying someone 40 or 50 years older and sometimes results in being pimped out. The second is to apply for political asylum, a process that can take up to four years and a status that is not often granted. The person granted such can never again return to Cuba while the regime is in power. The third option is to remain illegal with all of its attendant risks. After 11 months, the Cuban government essentially disowns you, and you become the proverbial "man [or woman] without a country.
(My translation and summary)
Geez, and I thought the Europeans were the enlightened ones! Read the original here.