Hi @Laedaa , is it possible that the AI who entered your borders chose an Expansionist culture? If you access the treaties overview in the diplomacy screen, empires with Expansionist affinities will have a red circle on the "Closed Borders" treaty. Hovering over it informs you about their affinity trait which makes trespassing possible without having to declare war. (note that this may be subject to change before launch)

Thank, yes, I and this country were Expansionists. I don't know about this expansionist's ability (a thought they can only buy outposts). 

While this was not a bug, there does appear to be one related to this.

As a player without expansionist, I could cross their closed borders with ease, so long as I gave a final destination within neutral or my territory. If I clicked on their territory, it would pop up with a box saying that I would have to declare war to enter that territory, and thus could not trespass as intended. If the pathfinding system plotted the route through closed territory to somewhere not in their territory, I could trespass.

Actually, I think that is an intended mechanic @Aloriel , as the troops have a debuff while they're in enemy territory, causing them to take 10% max hp damage each turn.

I could avoid the debuff by making sure that they ended their turn outside the closed territory. In the game I experienced this, there was a mountain range blocking easy access to one of my territories. I could go way around, or I could pass through purple's territory briefly. Purple already hated me and I massively out-teched them, so I didn't care about the trespasses. I just made sure to move from my territory to my territory through theirs without a turn break. Problem solved. Diplomatic crisis ignored. ;)