When a cockroach dies on its back, it is typically due to the ingestion of insecticide poison. The poison inhibits the cockroach's neurotransmitters, leading to muscle spasms that cause the cockroach to flip over. As the poison takes over, the cockroach loses muscular strength and is unable to flip back over to the right side.
While the common belief is that all cockroaches die on their backs, this is only true for domestic cockroaches and cockroaches that have been treated with insecticide. Domestic cockroaches are typically found dead on their backs due to the fact that linoleum and tile flooring in homes and buildings are difficult terrain for a cockroach to navigate.
The typical terrain for a wild cockroach consists of dirt, leaves and vegetable debris, allowing for a firm and steady stance. When a domestic cockroach slips on a tile floor and ends up on its back, it becomes immobile and can die from a lock of food and water.
Cockroaches are hearty insects that can actually survive for up to a month without their heads. Cockroaches do not have the same type of blood pressure system as mammals do. This prevents uncontrolled bleeding and allows the cockroach to remain mobile.