The gunman was “lying prone on his stomach.” He could have just been “prone,” and the writer could have saved four words for more drama.
“Prone” means lying flat, with your face toward the ground. If you’re face up, you’re “supine.” (One mnemonic: U are on your spine.) You don’t need to add “lying,” “on his back,” “on her stomach,” or any other modifiers, except perhaps for the location of the “prone” or “supine” person.
Writers are, um, prone to use the more familiar word, so “prone” appears more frequently when “supine” is meant. Almost no dictionary or usage authority accepts that substitution, though the Oxford English Dictionary notes of “prone”: “In strict use opposed to supine. In later use freq. more generally with reference to lying horizontal, or on the ground, without specific implication as to bodily posture.”
Sometimes, people are said to be “prostrate,” which can be imprecise. People “prostrate themselves” by kneeling before an altar, or they can be “prostrate,” lying on the ground, face up or face down, from humility, emotion, or devotion. “Prostrate” always carries an emotional attachment that “prone” and “supine” don’t have.
Whenever you see the phrase “lying prostate,” though, add that “r.” And if you see a “prostrate gland,” well, it’s lying down on the job.