https://www.frontpagemag.com/fpm/2022/06/what-will-happen-if-francis-resigns-william-kilpatrick/
But if Francis is not the pope, who is?
Those who deny the validity of Francis’s election say that Benedict is still the pope. They maintain that Benedict’s resignation was invalid. Benedict, they say, attempted a partial resignation: he intended to relinquish the ministerial (or administrative) duties of the papacy but not the office of pope. However, according to proponents of the invalid resignation theory, there is no provision in Canon Law or in Catholic doctrine for such a bifurcation of the papacy. The papacy, they say, is an all-or-nothing proposition. Hence, Benedict was guilty of a substantial error. And hence his resignation was invalid.
This may sound confusing and, indeed, many people did find Benedict’s drawn-out resignation speech to be quite confusing. It’s less confusing if one knows that before his election to the papacy, Benedict had for decades been part of a discussion among modernist theologians of ways to restructure the papacy.
According to the theory, Benedict seems to have concluded that he could resign his “active” role in the papacy while retaining a passive or contemplative role. He seems to have said as much in a papal audience given two weeks after his resignation: