In the world of dreams the rules of reality do not necessarily apply. Each dream is unique and it's a direct link to the soul and spirit. Psychology provides its own theories on what dreams mean, but so did tradition and the study of dreams for thousands of years before any relevant science had developed.
Dream Meanings - Cockroach
To dream of a cockroach forewarns of problems. Cockroaches symbolise disputes and enmities. Be careful at work. If, however, you dream that you are killing cockroaches, then everything will get better.