“Considering the special Divine Providence, and its manifestation in the past, with regard to the Holy See, the destruction of the Bishopric of Rome is indeed most improbable in the future. Still, it is an event within the sphere of possibility, and there does not appear to be any such certain, positive, and absolute guarantee for its perpetual per permanence as there is for that of the Catholic Church itself. Hence, theologians have supposed the extreme case of the extinction both of the city and See of Rome; and here their opinions are divided.

Some think that the Pope would then be bound to content himself with the title, together with the right of ruling the Roman See, should it be again revived much the same as in the case of titular bishops in partibus infidelium ; and that this would suffice for the actual succession of the Roman Pontiffs, as such, to the Primacy, since the title and right would still survive: so that whoever succeeded thereto would, as S. Peter s legitimate successor, have the Primacy over the universal Church. Other theologians incline to hold that, in such a case, a transfer of the Primacy to another See that the Pope might choose would be within the rights of the Vicar of Jesus Christ.” 

-Rev. Thomas Livius C.SS.R., St. Peter, Bishop of Rome, or the Roman episcopate of the Prince of the Apostles proved from the Fathers, history and archeology, (London: Burns and Oates, 1888, pg 284)

-All we need is a title and the right ✓
-this is the bare minimum for the actual succession, as the title and the right alone would survive ✓
-it would be as in the case of titular bishops in partibus infidelium ✓

Now let’s look at partibus infidelium.

Partibus infidelium, as per Merriam-Webster dictionary – “in the regions of the infidels” —used in a bishop’s title after the name of a diocese conquered by a power of another faith.

Shut the front door! Are you telling me that in case of pope splitting the papacy, he would still rule with the title and the right that would survive, as if he were in a diocese conquered by a power of another faith?

But get this, cardinal Manning is not shying away from a money quote for our times either:

“The writers of the Church tell us that in the latter days the city of Rome will probably become apostate from the Church and Vicar of Jesus Christ; and that Rome will again be punished, for he will depart from it; and the judgment of God will fall on the place from which he once reigned over the nations of the world. For what is it that makes Rome sacred, but the presence of the Vicar of Jesus Christ? What has it that should be dear in the sight of God, save only the presence of the Vicar of His Son ? Let the Church of Christ depart from Rome, and Rome will be no more in the eyes of God than Jerusalem of old. Jerusalem, the Holy City, chosen by God, was cast down and consumed by fire, because it crucified the Lord of Glory; and the city of Rome, which has been the seat of the Vicar of Jesus Christ for eighteen hundred years, if it become apostate, like Jerusalem of old, will suffer a like condemnation. And, therefore, the writers of the Church tell us that the city of Rome has no prerogative except only that the Vicar of Christ is there ; and if it become unfaithful, the same judgments which fell on Jerusalem, hallowed though it was by the presence of the Son of God, of the Master, and not the disciple only, shall fall likewise upon Rome.

The apostasy of the city of Rome from the Vicar of Christ, and its destruction by Antichrist, may be thoughts so new to many Catholics, that I think it well to recite the text of theologians in the greatest repute. First, Malvenda, who writes expressly on the subject, states as the opinion of Ribera, Gaspar Melus, Viegas, Suarez, Bellarmine, and Bosius, that Rome shall apostatise from the faith, drive away the Vicar of Christ, and return to its ancient paganism.* Malvenda’s words are: “But Rome itself in the last times of the world will return to its ancient idolatry, power, and imperial greatness. It will cast out its Pontiff, altogether apostatise from the Christian faith, terribly persecute the Church, shed the blood of martyrs more cruelly than ever, and will recover its former state of abundant wealth, or even greater than it had under its first rulers.”

Henry Edward Cardinal Manning, “The Present Crisis of the Holy See”, 1861, pg 87-88

Now let’s see the head count here:

-Rome apostatised from the faith ✓
-Rome drove away the Vicar of the Christ ✓
-Rome returned to ancient paganism ✓