Formal deposition is the culmination of the process that begins with, first individual or localized doubts, escalates into universal doubts, and then culminates in actual deposition.
This is where the sedeprivationist distinctions make so much sense. Theologians hold that widespread doubt based on grave reasons would justify Catholics withdrawing from submission. Other theologians state that in the face of such doubts, the Pope enters into the papa dubius state, in which he is essentially incapable of formally exercising his authority and binding consciences, since that ability derives from the certainty of faith Catholics would have regarding his status. So he goes into a "quarantine" state, as Father Chazal called it, until he's formally excised and materially ejected from the Church. That is the thinking behind my "sededoubtist" position. We are in this state of widespread positive doubt that renders him incapable of formally exercising authority, awaiting his ejection materially by the Church.
This is in fact the justification for the entire Traditional movement and apostolate.