One can be described as supine when lying face up ("his favorite yoga poses were always the supine ones"); or, if one is very passive or lethargic ("supine in the face of their threats and insults").
The adjective supine comes from a Latin word, supinus, which means “thrown backwards” or “inactive.” Whenever a person or animal is lying on its back, belly-up, it is supine. When your hand is open, palm-up, it is also supine. Supine can even describe a person who gives insufficient resistance, or who is lazy and ineffectual. "When Jack refused to object to the landlord’s repeated — and gouging — rent increases, he was supine."