What happened to Naegling and the energy in its gem?

Question

In Brisingr, Oromis's sword Naegling falls from his hand during an aerial battle immediately before he is killed. It would be one thing for a Rider's sword to be lost forever, but in the case of Naegling there is also a mind-boggling amount of energy stored in the diamond in its hilt.

During the century or so in which he hid with his dragon Glaedr in Du Weldenvarden, he, Glaedr, and several elves besides regularly added energy to the gem. The amount of strength the dragon alone could contribute every day would be staggering, even if it was only for one year; with all of them, over such a long period of time, Naegling's diamond must have been one of the most powerful objects in the world.

Given this, it's shocking to think that it was simply left where it fell and no one went to recover it. Nothing more is told in the series as far as I am aware, so what happened?

Answer 1

This is the subject of a future story, which will be published in Tales from Alagaësia volume 2 (2019? 2020?)

Q: Well another ‘no comment’ is coming because of this question: What happened to Oromis’s sword?

Christopher Paolini: Great question. I know exactly what happened to it. Something I’ll probably be writing about at some point, past that… no comment.

So it is still in your mind, it did go somewhere.

Christopher Paolini: Oh yeah, I don’t forget magical swords.
_{2013 Interview}

Q: What happened with the sword Naegling? Did someone take it along with all the power inside it?

Christopher Paolini: Yes.
_{March 2016}

Q: I always wanted to know the English translation of Oromis’ sword Naegling? Just as Eragon’s sword Brisingr is translated to mean “fire” and Zar’roc is translated to mean “misery” I figured Oromis’ sword must also have a meaning. I looked in the back of each book where the Ancient Language glossary was and I never found a translation for it!

Christopher Paolini: You're the first person to ask that! And I'd love to tell you, but unfortunately I can't because . . . it's an important plot point in a story I hope to write one day. Remember, Oromis dropped Naegling when Murtagh killed him? Whatever happened to it, I wonder? . . .
_{Reddit AMA May 2016}

Q: Hey this is a question that I have been thinking about sense the end of inheritance. It was stated that a ton of riders swords were found in galbatorix's personal items, was one of them undbitr, Broms sword? And was Oromiss sword in there too?

Christopher Paolini: Oromis's sword was not in that collection. No comment re: Undbitr.
_{Twitter November 2018}

Q: We know this is volume 1. . . . Is there anything you can tell us about what we can look forward to next?

Christopher Paolini: Heh. Right now I’m working hard on finishing up a massive sci-fi novel I’ve been focused on for a few years. After that, there are a whole host of stories I would like to write, including volume 2 of Tales from Alagaësia. In it, readers can expect some very new, very exciting stories, including—I hope—one about a dwarf detective and one about the fate of Oromis’s sword.
_{Penguin Books Australia interview January 2019}

So to recap:

• Someone took it after the battle
• It did not enter Galbatorix's collection
• Subject of a future story
• Expect to see the story in Tales from Alagaësia volume 2

Answer 2

It is likely Murtagh recovered it after the battle and took it to Galbatorix.

Christopher Paolini said that someone had it:

Q: What happened with the sword Naegling? Did someone take it along with all the power inside it?

A: Yes.
_{Q&As with Christopher - paolini.net}

And when they defeated Galbatorix, they recovered hundreds of swords.

They also recovered several hundred Riders’ swords: swords of every color and shape, made for both humans and elves. It was a breathtaking find. Eragon and Saphira personally carried the weapons to the castle where the Eldunarí were, in anticipation of the day when they would again be needed by Riders.
_{Inheritance - Pieces on a Board}

So while it is never said explicitly, this is the most likely scenario.