This is a discussion to be had with the owner - how do they want it to be handled , what are their wishes ? What end of life care plan they have put in place with the vet ? How will this be paid for ?
You may find some helpful advice from this previous thread discussing care of an elderly pet.
https://forum.trustedhousesitters.com/t/lessons-from-sitting-an-old-dog-or-any-animal-i-think