Usually, if a person dies while sharing a house with family, the ownership of any pets will be automatically passed on to those that they live with. This process is normally straightforward, so long as the family members agree to and are happy to take on the responsibility.
If you live alone, you will need to plan for the care of your pet after you’ve died. You can do this by adding a pet clause into your will or leaving written instructions. In fact, the simple act of telling someone you trust what you wish to happen to your pet after you die can be enough.