Answer: The Church has existed for years without a pope, and does so every time a pope dies. The Church has experienced a papal interregnum (i.e. period without a pope) over 200 different times in Church history. The longest papal interregnum (before the Vatican II apostasy) was between Pope St. Marcellinus (296-304) and Pope St. Marcellus (308-309). It lasted for more than three and a half years.[i] Further, theologians teach that the Church can exist for even decades without a pope.
EDMUND JAMES O’REILLY CRUSHES THE NON-SEDEVACANTISTS’ MAIN ARGUMENT ON THE LENGTH OF A PAPAL INTERREGNUM (PERIOD WITHOUT A POPE) BY TEACHING THAT THE CHURCH CAN EXIST FOR DECADES WITHOUT A POPE
Fr. Edmund James O’Reilly was an eminent theologian who lived at the time of Vatican I. Writing after Vatican I and its definitions on the perpetuity of the Papal Office, he taught that God could leave the Church without a pope for over 39 years – e.g., during the entire span of the Great Western Schism (1378-1417). Here is a quote from Father O’Reilly’s discussion of the Great Western Schism:
“We may here stop to inquire what is to be said of the position, at that time, of the three claimants, and their rights with regard to the Papacy. In the first place, there was all through, from the death of Gregory XI in 1378, a pope – with the exception, of course, of the intervals between deaths and elections to fill up the vacancies thereby created. There was, I say, at every given time a pope, really invested with the dignity of the Vicar of Christ and Head of the Church, whatever opinions might exist among many as to his genuineness; not that an interregnum covering the whole period would have been impossible or inconsistent with the promises of Christ, for this is by no means manifest, but that, as a matter of fact, there was not such an interregnum.”
Fr. O’Reilly says that an interregnum (a period without a pope) covering the entire period of the Great Western Schism is by no means incompatible with the promises of Christ about His Church. The period Fr. O’Reilly is speaking about began in 1378 with the death of Pope Gregory XI and ended essentially in 1417 when Pope Martin V was elected. That would be a 39-year interregnum (period without a pope). And Fr. O’Reilly was one of the most eminent theologians of the 19th Century.
It’s obvious that Fr. O’Reilly is on the side of those who, in rejecting the Vatican II antipopes, hold the possibility of a long-term vacancy of the Holy See. In fact, on page 287 of his book, Fr. O’Reilly gives this prophetic warning:
“The great schism of the West suggests to me a reflection which I take the liberty of expressing here. If this schism had not occurred, the hypothesis of such a thing happening would appear to many chimerical [absurd]. They would say it could not be; God would not permit the Church to come into so unhappy a situation. Heresies might spring up and spread and last painfully long, through the fault and to the perdition of their authors and abettors, to the great distress too of the faithful, increased by actual persecution in many places where the heretics were dominant. But that the true Church should remain between thirty and forty years without a thoroughly ascertained Head, and representative of Christ on earth, this would not be. Yet it has been; and we have no guarantee that it will not be again, though we may fervently hope otherwise. What I would infer is, that we must not be too ready to pronounce on what God may permit. We know with absolute certainty that He will fulfill His promises… We may also trust that He will do a great deal more than what He has bound Himself by His promises. We may look forward with cheering probability to exemption for the future from some of the trouble and misfortunes that have befallen in the past. But we, or our successors in the future generations of Christians, shall perhaps see stranger evils than have yet been experienced, even before the immediate approach of that great winding up of all things on earth that will precede the day of judgment. I am not setting up for a prophet, nor pretending to see unhappy wonders, of which I have no knowledge whatever. All I mean to convey is that contingencies regarding the Church, not excluded by the Divine promises, cannot be regarded as practically impossible, just because they would be terrible and distressing in a very high degree.”
This is an excellent point. Fr. O’Reilly explains that if the Great Western Schism had never occurred, Catholics would say that such a situation (three competing claimants to the Papacy with no thoroughly ascertained head for decades) is impossible – just like those today who say the sedevacantist “thesis” is impossible, even though the facts prove that it is true.
The Great Western Schism did happen, Fr. O’Reilly says, and we have no guarantee that worse things, that are not excluded by divine promises, won’t happen. There is nothing contrary to indefectibility in saying that we haven’t had a pope since the death of Pope Pius XII in 1958. There is everything contrary to the indefectibility of the Catholic Church in asserting that true popes could promulgate Vatican II, officially endorse false and pagan religions, promulgate the Protestant New Mass, and hold that non-Catholics don’t need to convert for salvation. Leaving the Church without a pope for an extended period of the Great Apostasy is the punishment inflicted by God on our generation for the wickedness of the world.
Prophecy of St. Nicholas of Fluh (1417-1487): “The Church will be punished because the majority of her members, high and low, will become so perverted. The Church will sink deeper and deeper until she will at last seem to be extinguished, and the succession of Peter and the other Apostles to have expired. But, after this, she will be victoriously exalted in the sight of all doubters.” 
 Denzinger 51-52e; Warren H. Carroll, A History of Christendom, Vol. 1 (The Founding of Christendom), p. 494; J.N.D. Kelly, Oxford Dictionary of Popes, Oxford University Press, 2005, p. 25.
 Fr. Edmund James O’Reilly, The Relations of the Church to Society – Theological Essays, 1882.
 Fr. O’Reilly, The Relations of the Church to Society – Theological Essays, p. 287.
 Yves Dupont, Catholic Prophecy, Rockford, IL: Tan Books, 1973, p. 30.
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