It was narrated tht 'Adiyy bin Hatim said:"I said: 'O Messenger of Allah, we are a people who hunt, and one of us may shoot his arrow but (the game) gets way from him for a night or two. What if he follows its tracks, and finds it dead with his arrow in it?" He said: "If you find the arrow in it, and you do not find any sign of predators, and you know that your arrow killed it, then eat it." (Sahih)
أَخْبَرَنَا زِيَادُ بْنُ أَيُّوبَ، قَالَ حَدَّثَنَا هُشَيْمٌ، قَالَ أَنْبَأَنَا أَبُو بِشْرٍ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ، عَنْ عَدِيِّ بْنِ حَاتِمٍ، قَالَ قُلْتُ يَا رَسُولَ اللَّهِ إِنَّا أَهْلُ الصَّيْدِ وَإِنَّ أَحَدَنَا يَرْمِي الصَّيْدَ فَيَغِيبُ عَنْهُ اللَّيْلَةَ وَاللَّيْلَتَيْنِ فَيَبْتَغِي الأَثَرَ فَيَجِدُهُ مَيِّتًا وَسَهْمُهُ فِيهِ . قَالَ " إِذَا وَجَدْتَ السَّهْمَ فِيهِ وَلَمْ تَجِدْ فِيهِ أَثَرَ سَبُعٍ وَعَلِمْتَ أَنَّ سَهْمَكَ قَتَلَهُ فَكُلْ " .
Nesai
The Book of Hunting and Slaughtering • Hadith 4300