If your budgie thinks he’s a statue, he might be standing very still, possibly with his eyes half-closed, as if he's frozen in place. This behavior could be due to a variety of reasons, such as feeling secure and relaxed in his environment, or simply being calm and content. It's usually a sign that your budgie feels safe and comfortable. However, if this behavior is accompanied by other signs of distress or health issues, it might be worth consulting an avian vet.