Sahih al-Bukhari 5485
Sahih al-Bukhari · Book 72: Hunting, Slaughtering · If the hunter hits a game but does not catch it till two or three days
وَقَالَ عَبْدُ الأَعْلَى عَنْ دَاوُدَ ، عَنْ عَامِرٍ ، عَنْ عَدِيٍّ ، أَنَّهُ قَالَ لِلنَّبِيِّ صلى الله عليه وسلم، يَرْمِي الصَّيْدَ فَيَقْتَفِرُ أَثَرَهُ الْيَوْمَيْنِ وَالثَّلاَثَةَ، ثُمَّ يَجِدُهُ مَيِّتًا وَفِيهِ سَهْمُهُ قَالَ " يَأْكُلُ إِنْ شَاءَ " .
And it has also been narrated by `Adi bin Hatim that he asked the Prophet (ﷺ) "If a hunter throws an arrow at the game and after tracing it for two or three days he finds it dead but still bearing his arrow, (can he eat of it)?" The Prophet (ﷺ) replied, "He can eat if he wishes."