Abdopt

Verb. (abdoption, abdopted, abdopting) Refers to the practise of acquiring an animal (usually a cat) by feeding and housing it, and then partially assuming ownership even though it clearly is domestic and had a previous owner. Often in an abdoption, the new self-proclaimed 'owners' are reluctant to take the cat to a vet clinic to check for a microchip or to put up missing pet flyers.

"My cat Fred is adorable! He just loves his jelly meat!"
"He's not your cat, you abdopted him."