FIrst of all, asylum is not a visa. It corresponds to a status as an 'asylee'.  When the girl's asylum gets approved, her spouse (i suppose it's you) gets derivate asylum status. Means, you also get the same asylee status upon filing a form I-730. But keep in mind, you two must have been married before your girl's asylum gets approved. Your fiance can marry you, then file the asylum. When she files for asylum, she has to put your informations too. If she files asylum as single, and if you guys marry before her interview, it's OK. You can also get asylee status. All she has to do is declare the changes in the interview. May be you both have to appear in the interview (not sure this part).