Oh, boy, would utilihtarian philosopher Peter Singer have "fun" with a New York Times column wrestling with how long to let an aged Fido suffer before putting him to sleep. Singer, a staunch animal rights advocate, would probably love to debate, possibly eviscerate, the columnist's comparing this issue to aged humans and the question of euthanasia. That's especially because Louise Aronson, besides being the owner of the pet in question, is a professor of medicine, specifically of geriatrics.
I would approach the issue from an angle somewhat like Singer might, re the dog, myself. The amount of attachment Dr. Aronson shows to her dog is cruel. It's also selfish.
She cares more about her attachment to Byron than she does for Byron itself.
At the same time, if a human were as bad off as Byron, shouldn't we be giving that person counseling about palliative care? Encouragement toward it, in fact?
It's cruel toward that person, even if they're still of reasonably sound mind, not to try to get them to detach somewhat from the desire to live, or "live," or exist, just a few more days or weeks. It's cruel toward others, as it continues to drive up the cost of health care and drain the personal resources of caregivers.
And, to not get loved ones of such a person to think that way themselves encourages their own selfishness.