Sirianism appears to be a major feature in what has been termed sedeimpeditism, which is distinguished from sedevacantism in that sedeimpeditists do not believe that the Holy See is vacant (sede vacante), but rather that a real legitimate Pope existed, but that he was impeded by outside forces (sede impedita) from taking his office.
Because some sedeimpeditists are even today not sedevacantists, some of them postulate that a true Pope in the Siri line may still exist somewhere in the world today, and thus they are also distinguished from conclavists, who are sedevacantists who took the next step and decided to elect their own Pope. A number of groups have attempted this step, including a group in Kansas, USA, who recognise David Bawden as Pope Michael I in 1990, and group around the (late) Elizabeth Gerstner. However, even if the Siri Thesis were correct insofar the Papacy became vacant in 1989 rather than 1958, these supposed elections would still not be valid according to canon law, which reserves the right to elect the Pope to the electors of the College of Cardinals. Hence, sedeimpeditists believe that the real papal succession would have to be preserved, most likely by a network of underground cardinals and bishops.
Sedeimpeditists who accept the Siri Thesis believe that Giuseppe Siri was the "Pope in Exile" long prophesied by Catholic saints (see "Catholic Prophecy" by Yves Dupont, Tan, 1971) during what they view as the current "Eclipse of the Church", as allegedly predicted by Our Lady of La Salette in 1846 (a vision approved by the Church). However, it may be asked whether Siri was truly in exile, as he continued to serve as Archbishop of Genoa and never questioned the validity of the known Popes. Siri was also known to be friends with John XXIII, although he did reportedly loathe Paul VI.
Although some sedeimpeditists may not agree with the Siri Thesis, or at least consider it as only one of a number of possibilities, they are in overall agreement with sedevacantists that starting with (usually) John XXIII, the civil structure of the Catholic Church has been controlled by heretics who could not possibly be Popes, and that there were enough modernist heretic cardinals to prevent real Catholics from undoing the revolution.
Read more about this topic: Siri Thesis