There are special laws allowing natives and citizens of Cuba, as well as their spouses and children, to obtain Green Cards.  You may apply for a green card under this law if you are Cuban and are in the United States one year after having been inspected, admitted, or paroled into the U.S. This means that if you entered the U.S. in a lawful manner, you may be eligible to become a Lawful Permanent Resident, even if you do not have an approved Family-Based or Employment-Based Immigrant Visa Petition. Furthermore, the cap on immigration do not apply to Cuban Adjustment applications.  If you entered the U.S. unlawfully, you may still be eligible to apply for lawful permanent residence under the Cuban Adjustment Act if the immigration service has paroled you into the United States.