In a jaw-dropping interview in the National Catholic Register with Edward Pentin, Cardinal Burke lays out clearly the situation. I highly recommend you go there and read it all, but I wish to reprint here, for your understanding, exactly what these four cardinals, and we should presume they are speaking for others, are doing.
Pentin: What happens if the Holy Father does not respond to your act of justice and charity and fails to give the clarification of the Church’s teaching that you hope to achieve?
Card. Burke: Then we would have to address that situation. There is, in the Tradition of the Church, the practice of correction of the Roman Pontiff. It is something that is clearly quite rare. But if there is no response to these questions, then I would say that it would be a question of taking a formal act of correction of a serious error.
Pentin: In a conflict between ecclesial authority and the Sacred Tradition of the Church, which one is binding on the believer and who has the authority to determine this?
Card. Burke: What’s binding is the Tradition. Ecclesial authority exists only in service of the Tradition. I think of that passage of St. Paul in the [Letter to the] Galatians (1:8), that if “even an angel should preach unto you any Gospel other than that which we preached unto you, let him be anathema.”
Pentin: If the Pope were to teach grave error or heresy, which lawful authority can declare this and what would be the consequences?
Cardinal Burke: It is the duty in such cases, and historically it has happened, of cardinals and bishops to make clear that the Pope is teaching error and to ask him to correct it.
There is another question coming. We will assume Edward Pentin did not ask it out of prudence or if was asked, it was certainly not answered. That question is this:
And if at that point, the Pope refuses to correct it; what then?
The answer is already above. Can you find it?