Cockroaches are known for their ability to survive without a head for a short period of time. This is because their nervous system is distributed throughout their body, and they can still breathe through small holes called spiracles located on their body segments. However, without a head, a cockroach cannot eat or drink, and it will eventually die of thirst or starvation. So while they can survive for a brief period without a head, they cannot live indefinitely without it.