If a pope resigned, would he still be infallible in matters of faith and morals?
If our Holy Father were to, heaven forbid, resign due to bad health and inability to exercise the requirements of his office, would he still, after resigning and having another man take his place, be able to speak infallibly in matters of faith and morals?
If the current pope resigned, he would no longer be serving as the pope. His successor would. He would retain his sacramental powers as bishop, but the juridical powers of his office would belong to his successor. The protection of the Holy Spirit, preventing the Church from teaching error in matters of faith and morals, belongs to the office of the papacy and not to the person in that office.