Say that a Pope becomes bedridden and so he cannot go out in public and does not have the stamina to perform other duties. Or he begins suffering from Alzheimer's and thus cannot remember that he is the Pope. At that point, the Pope is unable to continue his duties due to physical or mental illness.
Assuming that the Pope does not voluntarily resign due to his health (as Pope Benedict XVI did in 2013), would the Pope be removed from office and a new election be called? Or would he still nominally hold the role while others perform the duties of his office?