I was visiting the Blue Palace in Solitude when I decided that I didn't like thane Bryling, but I did like her outfit. Accordingly, I sneak-killed her and took her clothes.
Next thing I know, swords are being drawn and a fight breaks out, but not against me. It was the Solitude Guards versus Jarl Elsif, Falk Firebeard, Bolgeir Bearclaw and Erikur (all of whom are essential NPCs).
After a minute or so, the fight just sort of... stopped and everyone resumed their normal routine. But whenever I stopped sneaking and became visible again, the guards would go hostile on me-- even though according to my "Crime" menu, I hadn't incurred a bounty for the killing of Bryling. But while the guards were hostile to me, the Blue Palace NPCs were not, and they would again fight the guards.
This went on for several minutes until, inevitably, all of the guards lay dead as the essential NPCs had finally gotten the better of them. I hadn't lifted a finger during the fight, and again, I hadn't incurred a bounty.
Perhaps someone could explain what happened here? I understand why Elsif, Firebear etc would fight in my defense given that I was already made a thane by this point they seemed to like me, but why would the guards be hostile against me if my crime went undetected (i.e. no bounty)? It was just those guards within the Blue Palace, by the way. Once I left the scene, the other guards in Solitude didn't pay me any mind.

I will probably try today.