The Board of Immigration Appeals has determined that a Cuban paroled into the United States under section 212(d)(5) of the INA was not admitted to the United States as a refugee, and as such, cannot apply for adjustment of status under section 209 of the INA, which applies only to asylees and refugees. Moreover, though his parole was for the purpose of applying for asylum, his application for asylum was never granted, and therefore, he cannot take advantage of adjustment of status under section 209 of the INA as an asylee.
The full text of Matter of L-T-P- can be found here: