Wild dogs in certain countries may choose to move in with humans or leave when they feel like it. That's been true for most of their history. Hell, the main reason dogs in most English speaking countries don't roam free and join humans at will is thanks to a concerted effort to eradicate them because they hunt livestock and can hurt humans. Dogs are apex predators in their own right thanks to superior social abilities over cats. Dogs mostly chose to live with us, and many have the ability to survive without us.

Other common pets like rodents and parrots can also exist in nature just fine. Parrots are exceptionally intelligent and while rodents aren't, many are powerful enough to be a major pest to us humans. Cats are awesome, but they're only more autonomous than other pets in the modern era. Most other pets aren't allowed that level of freedom for their own safety and for ours.

If wild dogs or coyotes are common in your area, it might not be a good idea to even let them roam. Where I live, roaming cats have short life expectancies thanks to coyotes and cars.