What happens when an allergic person takes penicillin?

Varies. Some reactions are mild, such as hives alone. Others are more serious, with breathing problems and blood pressure drop. Some reactions (like some kinds of rashes) are not actually allergies, but different reactions that may or may not recur when you take the medicine. While it may be easier to just avoid penicillin, if it's important, you can find out if you have a "true" allergy by testing.
PCN Allergy. Maybe nothing, maybe a rash, GI upset, itching or maybe a serious allergic reaction called anaphylaxis. You must discuss with your allergist to determine the level of allergy and if you are truly allergic.