Adi bin Hatim (may Allah be pleased with him) asked: O Messenger of Allah (peace and blessings be upon him), one of us shoots game with an arrow and then follows it for a day or two, and finds the game dead with his arrow still in it. May he eat it? He said: "If he wishes, he may eat it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18906