Did you accidentally delete an aura or something? There is a way to restore a deleted or sold item. I wouldn't imagine that you could salvage an aura. I only know the PS4 controls but I am sure someone else could clarify the PC or Xbox alternatives. If you sold the aura there is a tab where you can buy back items you sold. If you deleted it somehow just hit "triangle" in an open space within your inventory. It shows several of the most recently deleted items. It will only allow you one restore per month or something like that, but it would definitely work if this is the case. Outside of that I am clueless about what you could be talking about unless you are talking about having an aura on one character but not the others. If that is the case see the posts above.
I think some of these none-feat related cosmetics should probably be account bound. So you can unequip them on one character and reuse them on another character on the same account. I have many very nice auras on my main, and I'm not getting the benefit.
Yea, I think that's what this is more about, being able to move auras across your toons when you might no longer want them locked to a specific toon and don't really wear them much. I imagine style sharing is probably more where this is going to come in to play though.