You may have heard the myth that a cockroach can live without its head. Well—it's true! According to the National Pest Management Association, a headless cockroach can live for weeks, moving about, reacting to touch, and exhibiting other basic behaviors. That's because the insect breathes not through the nose and mouth like we do, but through openings along the body. Not only would the decapitated body of the cockroach survive, but, at least for several hours, so would the separated head.