Cockroaches do bite, but it is not common for them to bite people. They can bite to feed on small particles and soft materials, and they usually use their jaws to chew or break off small pieces of food.
However, cockroaches can cause other health problems. They may trigger allergic reactions and spread microorganisms that can be linked to food poisoning and infections.
Although cockroach bites do not appear to be common, monitor the area if you think you were bitten. Wash the skin with soap and water, and avoid scratching to help reduce irritation or the risk of infection.