I have two cats.
If he fetches something in that is still alive it is not a present for me. He will attack anyone who goes near his prey/food. And that includes the live budgie he once brought in. And it's not a present, he eats the lot - often by my feet whilst I am in bed.
She once caught a bird that flew into the lounge window and was laid out cold on the floor. That was a present for me and is about the only time I can remember her catching anything.