I ran into another interesting situation. My king is currently Emperor of the HRE and inherited Lithuania (and Milan and Brandenburg) after having forced them into a Personal Union. That put me adjacent to and at war against the Golden Horde, but all of their provinces in the visible areas of the map are already occupied, mostly by Muscovy and Novgorod, with a few by Georgia and a few by kingdoms far to the east, but Muscovy occupies the two GH provinces adjacent to me. Basically, I can't fight the GH because they've got no armies in the area and no unoccupied provinces I can take, but they won't end the war with 0 war score even if I surrender and pay 5 years of heavy tribute. Meanwhile, England (which now holds half of France and various scattered provinces around the known world, making them the top military and naval threat) took an HRE province and released it to the Emperor, which now makes 4 illegal HRE provinces that I hold. The other 3 cannot be released because they have lost all of their cores during repeated annexations before being released to the Emperor as well, and now I cannot release the 4th while at war.
My king, who had a high enough diplomatic skill to inherit Lithuania and other countries upon his coronation, passed away only 3 years later, leaving the Empire to an infant heir (4/5/6 skills) and a regency council with 0 Diplomatic skill (6/3/5). That leaves me in the red for Infamy decay, and depending on how many Cardinals I have at the Vatican, generally leaves me either at +0.08 or +0.18 Infamy per year. I've already built an Embassy (-0.4 Infamy per year) and hired the best advisor I can with my Cultural Tradition to reduce Infamy (-0.15 per year), but that's insufficient to lower Infamy until the current heir reaches maturity in another decade or so. I'm fully expecting Burgundy to release another 1 or 2 illegal provinces in the next year or two, which will increase the rate of Infamy gain substantially. With the regency, I can't even declare war on the countries holding those Golden Horde provinces to hasten the end of the present war, and Muscovy in particular is currently gaining a mere 5 colonists per month with close to 500 in its highest occupied province, meaning around 8-9 more years until it defects to them.
The annoying aspects are that you cannot release a province that doesn't have a core, and that you cannot end a war against a country that you have no possible contact with unless you surrender and offer ridiculous incentives, sometimes even if you DO offer ridiculous incentives.
Don't you just love it when you've totally destroyed a country's army and navy, have around +10 war score, are currently besieging their capital, and they offer terms of surrender....YOUR surrender.....demanding provinces that they don't even occupy, demanding the release of vassals, and insisting on you handing them your entire treasury. The AI can demand provinces it doesn't occupy (and worse, the AI will occasionally accept those terms from another AI country), but the player is not even allowed to make such an offer, much less have it accepted. I've had a situation in one game where Venice would not even accept ANY terms short of ME surrendering, despite me having a +99 war score. Until I managed to sink their fleet (not a trivial task with a Naval Force Limit expanded to 3), they wouldn't agree to give up even a single ducat. Clearly, the AI does not play by the same rules as the player, nor does it treat the player the same as the other AI countries.