I live on a very busy little street in the centre of town so my cats don't get out. I don't get 'presents' and for that I am grateful. It is said that such gifts are given as a sign that you are worthy of their friendship - even though you are a pathetic hunter.
I know all about furry toys under, behind and even on top of furniture - a couple of times I have also found furry mice in the fridge and the washing machine. Being a mere human I am not even going to try and work out why they are stashed there.
Complex animals !