The Messenger of Allah (ﷺ) said to me: AbuTha'labah, eat what returns to you by your bow and your dog.

Ibn Harb's version adds: "The trained (dog), and your hand, then eat, whether it has been slaughtered or not slaughtered".
Sunan Abi Dawud Book 17, Hadith 13
← Previous Hadith I said: Messenger of Allah, I hunt with my trained dog, and with my untrained dog? He said: 'What you hunt with your trained dog, mention Allah's names (on it) and eat; and what you hunt with your untrained dog, and you find in a position that you slaughter it, then eat.

Sunan Abi Dawud Book 17, Hadith 12 Next Hadith → There was a bedouin called AbuTha'labah. He said: Messenger of Allah, I have trained dogs, so tell me your opinion about (eating) the animal they hunt. The Prophet (ﷺ) said: If you have trained dogs, then eat what they catch for you. He asked: Whether it is slaughtered or not? He replied: Yes. He asked: Does it apply even if it eats any of it? He replied: Even if it eats any of it. He again asked: Messenger of Allah, tell me your opinion about my bow (i.e. the game hunted by arrow). He said: Eat what your bow returns to you, whether it is slaughtered or not. He asked: If it goes out of my sight? He replied: Even if it goes out of your sight, provided it has no stench, or you find a mark on it other than the mark of your arrow.

He asked: Tell me about the use of the vessels of the Magians when we are forced to use them. He replied: Wash them and eat in them.

Sunan Abi Dawud Book 17, Hadith 14