What the hell, world? Why would a Pope get to resign, unless he was renouncing his Catholicism? That's a job that ends when you die. If and when you can't do it any more, other people do your work, but you stay Pope. You stay Pope until you're dead.
Same thing with Queen of England. Sure, sure, you can abdicate the throne, but that's renouncing your rights as a Royal. And seriously, does she actually rule anything? I thought that Parliament ran the country. Whatever. If she's too sick to leave the hospital - even if it's for the rest of her time, she stays Queen. She stays Queen until she has passed on, and then Charles will be King.
Why do people think that archaic, ancient positions should be subject to modern sensibilities? That's just crazy talk.