I thought of this question while rereading one of my favorite books, "A Canticle for Leibowitz" by Walter Miller. Before the start of the book, a nuclear war happens in the late 50s/early 60s. By the time of part one, in the 27th century, North America is in a state comparable to the Early Middle Ages. The Papacy has reestablished itself in the ruins of St Louis, renamed New Rome. The book does reference Catholic theology (Miller himself was a Catholic, and was inspired to write the novel by his involvement in the bombing of the abbey of Monte Cassino in WWII) such as the Pope mediating a dispute between the Dominicans and other holy orders on whether or not the Immaculate Conception also implied the Virgin Mary possessed preternatural gifts; however, Miller remains silent on how the 27th century Papacy claims apostolic succession from the first bishop of Rome (which itself is presumably destroyed in the the nuclear war), Saint Peter. This got me thinking: surely the Catholic Church had a plan for preservation of the succession should nuclear war break out in real life. If so, has the Church (or any of the other churches claiming apostolic succession such as the Eastern Orthodox or Anglican Churches) ever disclosed to outsiders their plans for preservation of the Church in general and the apostolic succession in particular? Or have they remained silent on the issue?
The Catholic Church doesn’t have any official line of succession, like America, nor is there any open “doomsday plans”. However, the process in which the Bishop of Rome has been selected has changed over the millennia. At one point it was through acclamation, Pope Fabian was elected when a dove landed on his head, for sometime only Cardinal-Bishops could elect the Pope, and now only Cardinals under 80 (at the Pontiff’s death) - in good standing - can elect the successor. Although, since Cardinals are in over 100 countries, the odds of this are very slim. If for whatever reason this all occurred, more than likely all of the living bishops, or Catholics, would come together and elect a Pope who would then rebuild his curia. It should be noted even if the new Pope went to Saint Louis, he would still retain the title ‘Bishop of Rome’ as occurred in the Avignon Papacy.