Fr. Chazal provides an assessment of Billuart in his book, Contra Cekadam, pg. 20. Bear in mind that Fr. Chazal is addressing Fr. Cekada:
"Billuart, OP (1685-1757), is very clear in his own De Fide: "Nowhere is it said that Christ continues to give jurisdiction to a manifestly heretical pontiff, because this can only be known by the Church and she can avail herself of another pastor. Nevertheless, the common sentence holds that Christ, by his special deposition, for the common good and tranquility of the Church, continues to give jurisdiction to a pontiff, even manifestly heretic, until he gets declared to be a manifest heretic by the Church." (diss. IV, III, #3.obj.2)"
"And in his 'de Fide de Regulis Fidei' Billuart pulls the carpet under the mantra of sedevacantism of ipso facto loss of office of a non-member of the Catholic Church: Billuart: "It is because in the case of heresy, and not in other cases, he loses the pontificate by the very fact of heresy: how could he stay a member of the Church if he is not a member?" (Addressing Fr. Cekada:) [I think you would not refuse to quote this part of the sentence, it sounds like you, reverend Father, but bear with us and pay attention to the rest, to what you always carefully omit]. Billuart con't: "That is why he is submitted to the judgment of the Church, not to be deposed, because he has already deposed himself through heresy and has rejected the pontificate, but to be declared heretical, and thus it may be known by the Church that he is no longer pontiff: before such declaration it is not allowed to deny him obedience, because he keeps then jurisdiction, not as a right,, as if he were still pontiff, but as a fact, God willing it thus for the common good of the Church." (diss IV, a., VIII, #2, obj. 2&6).