A pet allows you to own it or more specifically to think that you own it.
Collar it, tag it, microchip it... These things do not prove ownership.. That depends on the way you treat it.
A mistreated pet runs away.
A bored pet runs away.
A neglected pet runs away.
Even a caged pet would bolt as soon as it can manage to get free.
The pet that puts up with one or more of these things and stays does so if it's own free will. Because sometimes even when treated so badly or neglected/taken for granted, that pet loves and loves completely. It's loyal. It's not blinded by the love it feels but instead sees everything clearly. The love it feels, oh that horrid thing called love makes it stay and hope and we all know that there is nothing so cruel as hope.
That's the thing about pets, sometimes they bolt, sometimes they act out but it's only a few that actually leave... What does that say?