Mishkat al-Masabih 20 Game and Animals Which May Be Slaughtered كتاب الصيد والذبائح 4

وَعَنْهُ قَالَ: قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ: «إِذَا رَمَيْتَ بِسَهْمِكَ فَغَابَ عَنْكَ فَأَدْرَكْتَهُ فَكُلْ مَا لَمْ يُنْتِنْ» . رَوَاهُ مُسْلِمٌ

He reported God’s messenger as saying, “When you shoot your arrow and the animal goes out of your sight, eat it when you come upon it, provided it has not a stench.” (Bukhari and Muslim.)