Historically, sedeprivationists have held that the Pope who is not formally Pope may still be able to effect some acts validly, so that thereby the Church can be continued. These include appointing Cardinals, or incardinating Roman clergy, and at least some have argued that they would extend to appointing Ordinaries. Some of them denounced simple sedevacantism as heretical because it provided no mechanism for this, also because most sedevacantists held to the idea that the whole hierarchy had lost their offices and all episcopal sees were formally vacant.

More recently, some sedevacantists, although rejecting sedeprivationism, still seeing the need for the same appointments to be valid, believe that although the Pope is not the Pope in any sense, still these acts of his could be validated by supplied jurisdiction. Almost all can see that the Church cannot be continued otherwise, when all existing Ordinaries die, therefore such a theory is proposed.

But both of these seem impossible to reconcile with, among other things, Pope Paul IV's Bull cuм Ex Apostolatus, stipulating that

each and all of their words, deeds, actions and enactments, howsoever made, and anything whatsoever to which these may give rise, shall be without force and shall grant no stability whatsoever nor any right to anyone

Therefore, if the Pope is not the Pope, then those appointed by him have neither right nor stability, meaning bishops have neither office nor jurisdiction and Roman clerics cannot be incardinated by his acts, for they are null and void. The bishops and clerics, then, and the validity of their appointments stand or fall with the Pope's own claim. If he is really the Pope, then his enactments are valid and give rise to real bishops and clerics with a mission, ordinary jurisdiction and lawful incardination. If he is not, all his acts are as null and void as his Papacy itself.

The Church is indefectible ... in her monarchical constitution (principle 4), comprising governing power i.e., jurisdiction, hence Vatican I’s profession that Peter will have perpetual successors ... is indefectibility preserved if there is no pope since 1962 or if there is no one with ordinary jurisdiction whom the sedevacantists can point out as such?

There are only about 15 ordinaries left in the world appointed by Pius XII, if we include bishops appointed by John XXIII, their number increases by about 10, almost all of these near death and emeritus. When these die, the formal Apostolic succession has ceased, the ecclesia docens is no more, ordinary jurisdiction has not been passed on, and the promise of Christ has failed. Either that, or 50+ year sedevacantism is false.

But both of these seem impossible to reconcile with, among other things, Pope Paul IV's Bull cuм Ex Apostolatus, ...

Meanwhile, R&R is incompatible with the Church's indefectibility in a different way.

So it's pick your poison.

There are actually a number of the papa haereticus schools which suggest that heretical popes maintain jurisdictional authority despite losing other formal papal authority.

But both of these seem impossible to reconcile with, among other things, Pope Paul IV's Bull cuм Ex Apostolatus, ...

And cuм Ex also contradict's Billot's contention that acceptance by the world's bishops causes a sanatio in radice for defective elections.

There's a Catholic prophecy about how it will appear as if the Apostolic Succession had nearly ceased.

There are only about 15 ordinaries left in the world appointed by Pius XII, if we include bishops appointed by John XXIII, their number increases by about 10, almost all of these near death and emeritus. When these die, the formal Apostolic succession has ceased, the ecclesia docens is no more, ordinary jurisdiction has not been passed on, and the promise of Christ has failed. Either that, or 50+ year sedevacantism is false.

That's a logically false either ... or.  Since all these have NOT yet died, this does not mean that 50+ years of sedevcante are false.

This merely suggests that God will intervene soon to end the crisis.

I also still think that the Papal Mandate given to Bishop Thuc has some role to play in this.  There's every indication that he was given papal authority to consecrate bishops without explicit papal mandate, and this authority has never been revoked.

Well worth the read:

http://betrayedcatholics.com/wpcms/catacomb-catholics/faculties/

We know, ironically, that Our Lady tied the Vatican II disaster to Russia.

Quote from: Nishant

There are only about 15 ordinaries left in the world appointed by Pius XII, if we include bishops appointed by John XXIII, their number increases by about 10, almost all of these near death and emeritus. When these die, the formal Apostolic succession has ceased, the ecclesia docens is no more, ordinary jurisdiction has not been passed on, and the promise of Christ has failed. Either that, or 50+ year sedevacantism is false.

That's a logically false either ... or.  Since all these have NOT yet died, this does not mean that 50+ years of sedevcante are false.

This merely suggests that God will intervene soon to end the crisis.

I also still think that the Papal Mandate given to Bishop Thuc has some role to play in this.  There's every indication that he was given papal authority to consecrate bishops without explicit papal mandate, and this authority has never been revoked.

Thumbs Up, EXACTLY,  my point for what its worth.  

This entire scenario thread here reminds me so much of when Our Lord was walking on the water to His apostles, while a storm was raging, and Peter saw Him and he too with confidence in Our Lord, wanted to walk on the water.  Jesus told Peter to come, and Peter climbed out of the boat and started to walk across the water to Jesus.  The wind was blowing and the waves were high; Peter became afraid, he started to sink.  Jesus took Peter by his hand and said, "O you of little Faith, why did you doubt?"

Arnaldo Vidigal Xavier da Silveira, “Theological and Moral Implications of the New Ordo Missae." Circa 1975:

A more attentive examination of the question would reveal, nevertheless, that even on purely theoretical grounds, an important difficulty arises, which would consist in determining precisely what is the concept of pacific and universal acceptation by the Church. For such acceptation to have been pacific and universal would it be enough that no Cardinal had contested the election? Would it be enough that in a Council, for example, almost the totality of the Bishops had signed the acts, recognizing in this way, at least implicitly, that the Pope be the true one? Would it be enough that no voice, or practically no voice had publicly given the cry of alert? Or, on the contrary, would a certain very generalized, though not always well defined, distrust be sufficient to destroy the apparently pacific and universal character of the acceptance of the Pope? And if this distrust became a suspicion in numerous spirits, a positive doubt in many, a certainty in some, would the aforementioned pacific and universal acceptance subsist? And if such distrusts, suspicions, doubts and certainties cropped out with some frequency in conversations or private papers, or now and again in published writings, could one still classify as pacific and universal the acceptance of a Pope who was already a heretic on the occasion of his election by the Sacred College?