It would depend on the animal and the relationship between their guardian and the animal.

I would not qualify someone having a rescue dog that the dog would be a slave. It's more akin to having a child that you care for. In the same way I would not count a mentally disabled adult living with their parents a slave.

My current view on pets is that we should stop breeding cats and dogs just to keep them as pets especially seeing the horrendous conditions in which they are bred and the crazy things we select for while breeding to make them look cute while disregarding their well being (e.g. genetic disease that pure race cats or dogs have )

I however also understand that some animals are completely domesticated and cannot just be left alone. Taking care of them is fine for me.

Guardianship might be a good solutions for these cases.