Kai would have a trainer, being Teru-Masuta (or, well, just Teru for this)… but I can still see him being quite free-roaming, and ey’d let him wander and be out and is likely rarely ever in a pokeball if… he even has one.

It’s also likely he would of found Rin and Len’s egg when he was still a Zorua– and probably brought it to Teru for help, perhaps.