Guinea pigs usually sleep with their eyes open. The animals very rarely close their eyes, even when asleep. They rest their heads on the ground to sleep and sometimes sprawl with their legs outstretched.
Guinea pigs are vulnerable prey animals in the wild. They take frequent short naps throughout the day and night, and even then they do not close their eyes. This behavior is completely normal and is due to their low position on the food chain. It is simply a defense mechanism to keep them safe from predators at all times. Some guinea pigs do indeed close their eyes when they are asleep, but this behavior is not the norm. It is often a sign of deep relaxation and a feeling of security and does not signify ill health.