That literally doesn't mean anything in the context of the Papacy..... But I did do an experiment, with Investiture on the HRE the Emperorship will go to the pope if held by the pope. No papal influence on the heir.. Odd. So yeah, if you get an Investiture HRE, it will be unbreakable* to a certain point.
Now I've got to figure out how an AI Pope could possibly finagle an emperor title, to see if I can encourage it naturally. I am under the impression there are scripts making it so the Pope doesn't press claims on other Catholics. Killed a couple popes and the independence faction started blooming, 3500%+ revolt strength, so rapid successive Papal deaths would crush them pretty fast. I forgot that while Popes are OP as fuck, a bad Pope is typically an awful pope. The inheritance is so arbitrary they they're bound to explode just because of one really awful ruler. Curious to see what will happen if this revolt forces him out of the emperorship. Edit: The revolts are failing terribly, even with huge forces. Too many people absolutely love the pope no matter what. So far three empire-wide revolts one after the other, showing a majority of the vassals still want to break away.
Seems like the pope even gets +relation from Free Investiture. However that works.
Oh, and the Papacy currently has -5% Noble Vassal tax. I have no idea how this works. I think giving the Papacy the HRE really does break things.
Oh, and the pope personally taking any title higher than duke immediately turns it into investiture [not sure how to give duchy titles in the localization I'm using]. Even merchant republics of high rank. I don't think you can change them back either without outright destroying the titles, giving them even more permanence as theocracies.. No wonder you can't play as theocracies, they're kinda easy mode.