The law should be: Once an escaped non-pet animal has been on the loose long enough for the local news to show up and get it on video, it has claimed its freedom and gets to be a wild animal after that. You may transport it to its natural habitat if you want to and are able to do it safely and humanely—solely on the basis of the reasonable assumption that a free animal would choose to be in its natural habitat if it could—but you can’t return it to captivity. Ever!
I will accept some minor provisos to this new law, since obviously not all animals are the same; some might be harder for the news to find than others, and some might have a much harder time getting “on the loose” in the first place. A Galápagos tortoise, for example, has claimed its freedom literally the first moment nobody is looking directly at it, and the next person to look at it is required by law to transport it back to the Galápagos Islands. A loose snake will be difficult to find, even if it is large, and probably nobody will send a news van after it, so it’s not fair to make the snake wait around for news crews to get there; a loose snake has claimed its freedom after one hour. A Bengal tiger might possibly turn a preschool’s playground area into a lunch buffet, so the law will permit three hours for tracking down the loose Bengal tiger no matter how soon Action News shows up. After that, though, it officially has been released on its own recognizance, becomes a wild tiger, and cannot be recaptured, except for the purpose of transporting it to the jungles of like Bangladesh or wherever.
On a micro level this is good, because it means the sweet and gentle cow that escapes the stockyard and captivates Twitter for an afternoon will not be returned to its grim, unhappy wait for slaughter. It can go off and have adventures or whatever cows do. On a macro level it is also good, because it means that over time society will move in the direction of having herds of wild goats roaming the streets, which just objectively is cool.
Many people will say about the new law, This seems unsafe, I do not like the idea of a tiger wandering my neighborhood. I do not like the idea of circus clowns wandering my neighborhood, either! But I do not demand that all the clowns be rounded up and put in cages. The price of liberty is eternal vigilance (about wild tigers).
In conclusion, ungulates are free the very moment they breach containment. Goodbye.