The Siri claim as it now stands is that Siri was elected on October 26, 1958, accepted said election and took the name Gregory, making him the first Gregory XVII. He then was forced to resign or in some ay prevented from announcing his election to the world. Since foce was used, the theory is that such resignation is invalid. One can look elsewhere to determine if Siri's claim was actually true. However, let us assume for a moment it was.
On May 2, 1989, Siri died, leaving the Papacy vacant.