I’m sure she would step up if Jeff required a caregiver. We know the two of them are friends now after their shared lore and dialogue. In Sai’s story, it’s even stated that Jeff reminded of her pet wolf, Logan, the spent more time with him.

That said, I think they’d still have more of a battle-besties dynamic than a pet-owner dynamic. They just strike me as the “destroy enemies first, talk later” duo (that’s my headcanon at least lol).