I had the same thing but with a hawk. 2 different ones in fact. The first, on the way to the very first nord dungeon close to riverwood I killed a few hours into the game. I came back recently, saw the hawk fly around again, shot him with arrows about 5 times, he kept flying around.. With 5 arrows sticking around him, but NOT in him. Second hawk in riverwood, same thing happened. Must be a bug. I'll take screen shots if needed, it's kind of a funny sight actually.