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