And it has also been narrated by ʿAdi 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."  

أَنَّهُ قَالَ لِلنَّبِيِّ ﷺ يَرْمِي الصَّيْدَ فَيَقْتَفِرُ أَثَرَهُ الْيَوْمَيْنِ وَالثَّلاَثَةَ ثُمَّ يَجِدُهُ مَيِّتًا وَفِيهِ سَهْمُهُ قَالَ يَأْكُلُ إِنْ شَاءَ  

Messenger of Allah, one of us shoots at the game, and follows its mark for two or three days, and then finds it dead, and there is his arrow (pierced) in it, may he eat it? He said: Yes, if he wishes, or he said: he may eat if he wishes. (Using translation from Abū Dāʾūd 2853)   

أَنَّهُ قَالَ يَا رَسُولَ اللهِ إِنَّ أَحَدَنَا يَرْمِي فَيَقْتَفِي أَثَرَهُ الْيَوْمَ وَالْيَوْمَيْنِ فَيَجِدُهُ مَيِّتًا وَفِيهِ سَهْمُهُ أَيَأْكُلُ؟ قَالَ نَعَمْ إِنْ شَاءَ أَوْ قَالَ يَأْكُلُ إِنْ شَاءَ