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." (FR)
English reference (FR): Book 12, Hadith 1375 (FR)
Arabic reference (FR): Book 12, Hadith 1335 (FR)