Can eating a piece of hard cheese lead to illness?

It isn't likely. Although the raw milk used to make hard cheeses may contain salmonella or E. coli, hard cheeses undergo pasteurization in order to kill these pathogenic bacteria.
 
Additionally, hard cheeses are ripened--or aged--cheeses. Cheeses ripened for at least 60 days generally lack the moisture required to support pathogen growth (the type of bacteria that cause illness). For the same reason, they don't readily support the growth of spoilage bacteria (the ones that cause bad taste, etc.) However, hard cheeses don't last forever. Although relatively dry, they eventually grow moldy. Fortunately, proper storage of hard cheese can delay mold growth and extend shelf life--meaning the amount of time the cheese will keep.
 
Source(s):
National Dairy Council "Cheese"