Church corruption and papal infallibility

Reading all the corruptions in churches and some popes in history, I wonder how it affects the doctrine of papal infallibility and apostolic succession claim of the Catholic church. Who is or represent the real pope during the Great Schism when there were more than one pope? I wonder what is Catholic church's explanation on this.

Here is what I found on the wikipedia on papal infallibility:
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Papal infallibility is the dogma in Catholic theology that, by action of the Holy Spirit, the Pope is preserved from even the possibility of error when he solemnly declares or promulgates to the universal Church a dogmatic teaching on faith or morals as being contained in divine revelation, or at least being intimately connected to divine revelation. ...
This dogma, however, does not state either that the Pope cannot commit sin in his own personal life nor that he is necessarily free of error, even when speaking in his official capacity, outside the specific contexts in which the dogma applies.

This doctrine was defined dogmatically in the First Vatican Council of 1870.
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Interesting position! Can this be compared to the inspiration of the Scripture? Prophets and apostles are not perfect, yet inspired for inerrancy for the portion of the Scripture they wrote. If this is the case, should Pope's proclaimation go through the same standard as we used for the canon of the Scripture? In this case, any pope is also more "inspried" than any of the authors of the Bible because we do not have such claim for any of them.
I also wonder if those corrupted popes in the history made any wrong claims.

I think we will learn more about reformers' position on apostolic succession later.