Narrated Adi bin Hatim:

The Prophet (ﷺ) said, "If you let loose your hound after a game and mention Allah's Name on sending it, and the hound catches the game and kills it, then you can eat of it. But if the hound eats of it, then you should not eat thereof, for the hound has caught it for itself. And if along with your hound, joined other hounds, and Allah's Name was not mentioned at the time of their sending, and they catch an animal and kill it, you should not eat of it, for you will not know which of them has killed it. And if you have thrown an arrow at the game and then find it (dead) two or three days later and, it bears no mark other than the wound inflicted by your arrow, then you can eat of it. But if the game is found (dead) in water, then do not eat of it."

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."