The Apostolic See was pure and will always remain pure of all doctrinal error which can condemn a soul to hell, because this See is the immutable rock on which the Church is built. The defection of this See (which is impossible) would mean the defection of the Church (which is also impossible). Never has a legitimately elected Pope uttered heresy, but there have been many counterpopes who have reigned in Rome.
Pope Agatho proved this when he wrote that none of his predecessors, even the most minim among them, have allowed the catholic faith to be perverted in the Roman See, and that this can never happen in the future. The Apostolic See remains unsullied.Tolle papam, tolle missam, tolle ecclesiam.
When one takes away the Pope, he takes away the Mass, and ultimately the Church.
But the Church does not cease to exist, and neither can her divine constitution (which necessarily means all her elements of apostolicity and her four marks) be impaired. The mark of visibility, however, means that the Church is a perfect society of tangible human beings who thus have the capacity to be seen with the carnal eye. It does not mean that they have to be seen on television to keep this mark intact.
So, simply because you and I do not know where the successors of the apostles are residing, does not mean that they do not exist. To keep the mark of visibility intact, it is merely required that the Church remains made up of visible human beings, and does not become a pneumatic 'bond' between all who claim to be christians, which is the protestant error to which this mark is directly opposed.
We are thus required to believe that legitimate papal electors have been provided and exist today, because the First Vatican Council has defined that Christ has willed there to be pastors until the consummation of time. There have been many counterpopes before the 20th century, so this situation knows precedent.
"This dismal fate of Rome is not contrary to the promises made to the Church and the Apostolic See to persevere in faith.... Church always remains visible, even if She would be forced to flee to the mountains and hiding mostly in caves and deserts. “
“The apostasy of the city of Rome from the vicar of Christ and its destruction by Antichrist may be thoughts very new to many Catholics, that I think it well to recite the text of theologians of greatest repute. First Malvenda, who writes expressly on the subject, states as the opinion of Ribera, Gaspar Melus, Biegas, Suarrez, Bellarmine and Bosius that Rome shall apostatize from the Faith, drive away the Vicar of Christ and return to its ancient paganism. ...Then the Church shall be scattered, driven into the wilderness, and shall be for a time, as it was in the beginning, invisible; hidden in catacombs, in dens, in mountains, in lurking places; for a time it shall be swept, as it were from the face of the earth. Such is the universal testimony of the Fathers of the early Church.”
Certainly, Cardinal Manning did not mean to say that the Church would lose one of her marks (visibility). He makes a distinction between actual visibility and the mark of visibility. The first means that we do not see the Church on television or the newspapers. The latter means that the Church keeps her mark, which means the capacity to be seen.
Let us try not to make this a flame war. Discussions such as these have been heated in the past, and I admit that I have shared in the guilt. But let us avoid such things now. Charity is still the domain of Christendom, even though the masons have usurped the word and perverted it.