Like Affable Geek states...this is more historically concrete than one might think.
I think the basic 2 questions you are getting at (someone correct me if I'm wrong) are:
Question 1 - What would (should) happen if a Roman Pope promulgates, decrees, or endorses a heretical doctrine?
Answer - He would be anathametized as an heretic in an Ecumenical Council:
Pope Honorius I of Rome was the Pope of the Church of Rome from 625 to
638. While successful in missionary and administrative activities he is remembered for his condemnation as a heretic at the Sixth
Ecumenical Council of 680/681, after his death.
It was in his support of Patriarch Sergius I during the Monothelite
controversy that Pope Honorius gained his notoriety in history. About
the year 634, Patr. Sergius I raised, in a letter to Honorius, the use
of the expression "one operation/one will" in an attempt to reconcile
the differences between the Orthodox and the Monophysites following
the condemnation of Monophysitism at the Fourth Ecumenical Council in
Chalcedon. The term was raised when emperor Heraclius made use of the
expression in refuting the Monophysites during a visit to Armenia. Its
use was questioned and then referred to Patr. Sergius who, not ready
to make a decision, referred the question to Pope Honorius. Honorius,
in his reply to Sergius, while concurring on the questionability of
the expression, and also of "two operations" as being Nestorian, left
his explanation concerning Monothelitism unclear and sounding as if he
endorsed Monophysitism while giving support to Sergius...
...[T]o settle the issue, in 680, the Sixth Ecumenical Council met in
Constantinople under the auspices of Eastern Roman emperor Constantine
IV. The council condemned Monothelitism and, after deliberating
over the doctrinal letters of Sergius and Honorius that were found
quite foreign to the apostolic doctrines, anathematized as heretics
Honorius and Sergius as well as Cyrus of Alexandria, Paul II, Peter
of Constantinople, and Theodore of Pharan. (Orthodoxwiki)
Question 2: Are Catholics required to accept whatever the Pope promulgates, decrees, or endorses as a divinely revealed dogma of Truth no matter what?
Answer - Yes...according to Vatican I at least:
Wherefore we teach and declare that, by divine ordinance, the Roman
Church possesses a pre-eminence of ordinary power over every other
Church, and that this jurisdictional power of the Roman Pontiff is
both episcopal and immediate. Both clergy and faithful, of whatever
rite and dignity, both singly and collectively, are bound to submit to
this power by the duty of hierarchical subordination and true
obedience, and this not only in matters concerning faith and morals,
but also in those which regard the discipline and government of the
Church throughout the world...
...[T]his is the teaching of the Catholic truth, and no one can depart
from it without endangering his faith and salvation...
...[S]ince the Roman Pontiff, by the divine right of the apostolic
primacy, governs the whole Church, we likewise teach and declare that
he is the supreme judge of the faithful, and that in all cases which
fall under ecclesiastical jurisdiction recourse may be had to his
judgment. The sentence of the Apostolic See (than which there is no
higher authority) is not subject to revision by anyone, nor may
anyone lawfully pass judgment thereupon. And so they stray from the
genuine path of truth who maintain that it is lawful to appeal from
the judgments of the Roman pontiffs to an ecumenical council as if
this were an authority superior to the Roman Pontiff...
...[T]herefore, faithfully adhering to the tradition received from the
beginning of the christian faith, to the glory of God our savior, for
the exaltation of the Catholic religion and for the salvation of the
christian people, with the approval of the Sacred Council, we teach
and define as a divinely revealed dogma that when the Roman Pontiff
speaks EX CATHEDRA, that is, when, in the exercise of his office as
shepherd and teacher of all Christians, in virtue of his supreme
apostolic authority, he defines a doctrine concerning faith or morals
to be held by the whole Church, he possesses, by the divine assistance
promised to him in blessed Peter, that infallibility which the divine
Redeemer willed his Church to enjoy in defining doctrine concerning
faith or morals. Therefore, such definitions of the Roman Pontiff
are of themselves, and not by the consent of the Church,
irreformable. (Pastor Aeternus)
This question brings attention to the fact that the Roman Catholic Church perches upon this very doctrine, namely, Papal Infallibility. In other words, it is this doctrine that separates the Church from all other Churches - especially the Eastern Churches.
Rome claims that whenever former Popes made heretical statements or accepted heretical doctrines...they were not using all of the required ingredients for being infallible.
How would a situation similar to that of Pope Honorius' be explained or justified by Rome in the future?