How can black mold effect someone who has asthma?

Badly. Black mold can cause significant pulmonary effects in someone who doesn't have asthma. So, someone with already-impaired airways can certainly have an exacerbation of their asthma if exposed to black mold.
Black Mold&Asthma. Black mold can exacerbate asthma symptoms and cause acute asthma as well, in people who are allergic to mold.

Related Questions

How can black mold effect someone who has asthma or other lung diseases?

Trigger or other. Mold spores can trigger asthma, or can lead to an asthma like disease (allergic bronchopulmonary aspergillosis). Get the mold removed from your home and see if there is improvement, and have yourself tested for abpa. Read more...