Well, after searching far and wide, I wasn't able to find on the web any trigger or event that would make Bryling UNessential. Many have searched for this as well based on the sheer amount of folks looking for ways to get her special/ unique apparel, the fur trimmed cloak,boots and fine gauntlets.The only other way to go about obtaining anything similar from an apparel standpoint would be offing U. Stormcloak.
After starting my secod charachter I found out about the sometimes essential Bryling. I went back to my first character who was about 80hrs in and was able to off her easily in the Blue Palace. I heard rumors that the Dark Brotherhood quests were tied to her...so I tried with my second charachter. I wasn't able to kill her after that quest line. Some have hinted after the Thieves guild questline you are able to....alas is was not true.
So I reverted back to an old save and took three days to finish both questlines. She was able to be killed after these two quest lines were done! So to rock the fur trimmed cloak...finish the guild quests and you'll have them!

