Well he likely didn't shoot it to eat it. If he did he would have made sure it was dead.
He ran off because a hefty southern woman walked out of the house with a SPAS12, lol jk. I hate cats, when I was a kid stray cats used to steal our toys. When we were playing catch one of us would drop the tennis ball and the cat would drop it in the suage(no spell check :c). It took all 4 of our balls... Im sure I wouldn't shoot it with an arrow though :c. He prob did it though cause the owner pissed him off. It happened with a dog(burned alive).