First, to answer the original question:
The matter of infallible doctrinal teaching is one of knowledge, not free will. The pope is given the ability to, without error, interpret the scriptures and the sacred traditions with perfect clarity. The free will issue, then, comes in only on speaking: does God allow the pope the free will to lie? The answer is yes, the pope COULD attempt to lie, and has the free choice to do so. However… (i’m going to drop a quote from another poster in here)
If he tried to deliberately veer into error would God make him mute? Strike him dead? Luckily, it doesn’t seem that any Popes have chosen to experiment.
Actually, the fact that it “doesn’t seem that any Popes have chosen to experiment” is incorrect. Several popes have, for reasons unkown, cancelled their ex cathedra statements and never made them.
Honorius embraced heresy privately, but never did feel compelled to make an official statement in support.
Pope St Agatho, who refused to condemn Honorius’ heresy, died suddenly before the end of the council in question. The new Pope, Leo II, approved the condemnation, but with the special note that it was NOT for teaching heresy, but for his failure to reject it.
So yes, popes have died in the past when their official statements would not have matched with the will of God through His church. I don’t think St Agatho was the only one with plans to make an infallible declaration who didn’t live to see the chair, either, but I’m at work so my references are limited here
