I imagine I'd find a way to do it as responsibly as I could. I'd think about my health, average lifespan of the animal, look at sponsoring options, talk to loved ones who might be genuinely interested in being godparents, etc. etc.
I think even anticipating the possibility of a pet outliving someone is a responsible thing to do. Nobody can really guarantee that their pets won't be orphaned, that we'll lose our health, etc. but I think responsibility is responding to needs that can reasonably be anticipated as best we can.
if i knew i couldn't take care of a pet anymore (like if i had terminal illness or were elderly like CD's in-laws), i'd donate it to a good home or surrender it at a shelter. i would feel awful of course, but these things happen.
i don't know if anyone here is adopting any tortoises because i know those can outlive humans by a long shot.
It's probably not ideal emotionally for animals to change homes/families regularly, but if you plan for the animal's future, I don't think it's irresponsible in other ways. Pets need homes and old people benefit from their company, etc.
I would really only be thinking about this if I were an elderly person thinking of adopting a pet who lives 7+ years, which I am not. I think people should do what would make them happy. Pets can always be relocated to another owner. If I were 75 and a dog were really important to my mental health, I would do it with an agreement of new owner should I pass before.