This is an interesting question. If there is free will involved in the electors and free will involved in the actual Pope, then why coudn;t a Pope say "this is an Ex Cathedral statement and then proceed to error? Would God literally strike him down or dumb?
Actually, there are some examples where something like that seems to have happened.
Pope Clement VIII - 1605 A.D.
“In the spring of 1605, Pope Clement VIII, after a careful study of the opposing positions on the question of grace and free will, was about to render an official decision approving the so-called ‘Thomist’ position and condemning that of Luis de Molina, S.J. But before he could promulgate the already drafted condemnation, he died.”
catholic.com/thisrock/1995/9501fea3.asp
Pope Sixtus V - 1590 A.D.
After a team of Bible translators presented a revision of the Vulgate to Pope Sixtus V, “[the pope] angrily announced he would personally revise the Vulgate. He declared, ‘We, weighing the importance of the matter, and considering carefully the great and singular privilege we hold of God, and our true and legitimate succession from Blessed Peter, Prince of the Apostles…[are] the proper and specially constituted Person to decide this whole question.’ ”
“Ill equipped for the task, Sixtus eliminated all the work done by the former commission, and started fresh. Unfortunately his abilities to translate, edit and make all the appropriate decisions were beyond his capabilities and the result was an error filled translation presented to the cardinals in early 1590.” According to Patrick Madrid, “If Sixtus had formally promulgated this distorted version, it would have allowed a strong case to be argued against the doctrine of papal infallibility since the Pope would have fulfilled the three requirements layed out by Vatican I for an infallible teaching.”
“Expectation was at a boiling point. The news in Rome had it that the official promulgation would happen any day. Advance copies of the new Vulgate had been bound and delivered to all the cardinals in Rome along with advance copies of the bull officially publishing it. Everything was ready for the pope to promulgate the new version. Nothing could stop him.”
“But at the last moment Sixtus, whose health and vigor were never questioned, took to his bed, dying on August 27, 1590 after a brief illness. The Holy Spirit’s promise to guide the Church to all truth seems to have been fulfilled again.”
Much of the above is quoted from Patrick Madrid, Pope Fiction, pages 242-51. The rest comes from
catholicfaithandreason.org/papal-infallibility.html
Isn’t Church History wonderful?