I just received an affirmative response on my Petrine Privilege case and was married almost 4 weeks ago (tomorrow is our one month anniversary).
You cannot apply for it until there is someone that you want to marry in the Catholic Church, it will not be granted if you do not have someone you wish to marry, and my diocese wouldn’t even submit it until I was engaged. My tribunal told me it was taking almost the entire 6 months that they say it will once it was received in Rome. I submitted the first paperwork in March, it was in Rome by May 15th and my affirmative response was given on Sept 15th-ish. I don’t have the paperwork here with me so the exact days are off.
It is not specific to WHO caused the marriage to fail, but more what caused it to fail. There also seemed to be a lot of questions regarding if scandal would be caused were it dissolved. I think this is especially the case if one party were Catholic and the unbaptized wants to become Catholic and they are still members of the same parish. If the marriage was consummated after the unbaptized party became Christian, then you need a decree of nullity because it became a Sacramental marriage at that point.
I guess I’m not sure what else to say. It was expensive in my diocese, but it was 100% worth it, not to mention that I know a lot goes into it. I had to have 4 blood relative witnesses (I was the unbaptized one), answer a litany of questions and he also had to respond to a questionnaire.
Any other questions?