Abu Tha'laba reported Allah's Messenger (ﷺ) having said this: If you shoot with your arrow and (the game) goes out of your sight and you find it (later on), then eat that if it has not gone rotten.
Hadith Referenceصحيح مسلم / كتاب الصيد والذبائح وما يؤكل من الحيوان / 1931