There has been much debate about how the Church would proceed, if all of the Cardinals (or other ordinary electors of the Pope) would cease to exist. We have seen that this is indeed the case. Canonists hold that the Church always has a way to elect a Pope. Their debate is over how the Church would proceed.
Even when there were ordinary electors, others have intervened and chosen the Pope, such as Emperor Henry III, who choose three in a row, the last being Pope Saint Leo IX. The fact that these elections were never challenged, indicates that in so important matter, nothing but heresy on the part of the one apparently elected, invalidates the election of a Pope. Saint Alphonsus states: “It doesn’t matter that in past centuries some pontiff has been elected by fraud: it suffices that he has been accepted after as pope by all the Church, for this fact he has become true pontiff.”
Papal Elections Brought Down to Date By Joseph P. Donovan, C.M., J.C.D., 1945: “It (Pope Pius XII’s Papal Election Law) visualizes every possible contingency, and provides for it; it takes away every pretext for contesting a Papal election on the ground that it was procured by simony or that the Conclave was broken; it makes sure that the required two-thirds vote does not include the ballot of the Pope-elect by demanding as a safeguard a two-thirds majority plus one.”
Father Staislaus Woywod in his commentary on Canon Law comments (volume 1, pages 361-2): “An exception from the rule of 729 (in regard to simony) is made in favor of the election of the Supreme Pontiff: to remove all pretext of attacking the validity of the election of the Roman Pontiff, this election, though obtained through simony, is declared valid by the Constitution “Vacante Sede Apostolica” of Pope Pius X, December 25, 1904.”
1947, Origins of the Great Schism, page 159 by Ullman: “The cardinals, says Baldus, by their consent to the election of a certain individual as pope, thereby remedy every defect which would otherwise make unfit or unsuitable for his office, even if he were excommunicated or a notorious concubinary priest or an infamous murderer. “The apostolic see either makes holy or it receives a holy man.” Accordingly, there is no doubt that the cardinals have it in their power to clear the candidate of all irregularities-except one, and that is persistent heresy.”
Msgr. Charles Journet, Church of the Word Incarnate, 1955: (5) Validity and certitude of election. The election, remarks John of St. Thomas, may be invalid when carried out by persons not qualified, or when, although effected by persons qualified, it suffers from defect of form or falls on an incapable subject, as for example one of unsound mind or unbaptized.
But the peaceful acceptance of the universal Church given to an elect as to a head to whom it submits is an act in which the Church engages herself and her fate. It is therefore an act in itself infallible and is immediately recognizable as such. (Consequently, and mediately, it will appear that all conditions prerequisite to the validity of the election have been fulfilled.)
Acceptance by the Church operates either negatively, when the election is not at once contested; or positively, when the election is first accepted by those present and then gradually by the rest (cf. John of St. Thomas, II-II, qq. 1-7; disp. 2, a. 2, nos. 1, 15, 28, 34, 40; pp. 228 et seq.). (Emphasis mine)
“When any bishop is elected Supreme Pontiff, either by cardinals or by the people according to the times, from whom does he obtain the supreme power of jurisdiction? From Christ, of course…” (Speech given by the Bishop of Grenada at the 22nd Session of the Council of Trent; Concilium Tridentum Editio Gorresiana, Vol. IX, # 50; 1919)