Tamiyo, the Moon Sage

The ability can target a tapped permanent. If the targeted permanent is already tapped when it resolves, that permanent just remains tapped and doesn’t untap during its controller’s next untap step.

Cards that are put into your graveyard can be returned to your hand by the emblem’s ability even if they were never in your hand.

Tamiyo’s first ability tracks the permanent, but not its controller. If the permanent changes controllers before its first controller’s next untap step has come around, then it won’t untap during its new controller’s next untap step.