Sahih Bukhari Volume 7, Book 72, Hadith 5487

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 "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 replied, "He can eat if he wishes."