Yes, cockroaches shed their skins, however this isn't uncommon amongst other insects, especially when developing into their mature form, however cockroaches can do this several times a year, growing larger each time.The newly shedded cockroach is white with black eyes and is soft until after 8 hours where it's shell will harden and form colour. Their cast off skin and waste byproducts are allergens that can trigger allergic reactions, asthma and other illnesses, especially in children.