Adi bin Hatim (may Allah be pleased with him) says that the Prophet (peace and blessings be upon him) said: "When you send your dog after game with the name of Allah, and the dog kills the game and does not eat from it, then eat the game. If the dog eats something from the game, then do not eat the game, because the dog has hunted it for itself. And when other dogs join your dog over which the name of Allah was not mentioned when they were sent, if they kill the game and hold it, that is, keep it, then do not eat, because you do not know which one killed it. If you shoot game with an arrow and find that same game with your arrow after one or two days, then eat if you wish; if it falls into water and dies, do not eat."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18904