Abu Tha'labah (RAA) narrated that the Messenger of Allah (ﷺ) said:
"When you shoot your arrow and the game has gone our of sight, eat it when you come upon it, provided it has not become rotten." (RU)
English reference (RU): Book 12, Hadith 1375 (RU)
Arabic reference (RU): Book 12, Hadith 1335 (RU)