religious hypothetical

What would happen in the Catholic church if the Pope lost all higher brain function, was still able to breathe on his own but had to rely on a feeding tube to survive?

(Note: better minds than yours have already asked "what's the difference?" so don't even bother to go there.)

I can't possibly imagine that anyone would make the decision to take him off life support. But who would run the place? Is there such a thing as Acting Pope? How does the chain of command work?