Your cat plays outside during the day on Pesach. You see your cat rolling around in the dirt that has Chametz that was deposited by Gentiles walking on the street. The cat also decides to carry a bag of Chametz in its mouth and runs into your house with the bag.
Do you need to brush the cats fur and inspect it for Chametz even if it's not clearly visible?
What should you do with the bag of Chametz if the cat brings it into your house during Yom Tov? Is the Chametz muktzah, so you can't move it? If the cat has eaten the Chametz on its own, have you violated owning Chametz on Pesach, or is this nullified by the fact that you didn't physically own it since you didn't move it, and now it's gone, anyway?