Eragon and Saphira die. Arya doesn't cope well.
(For context, Eragon defeats Galbatorix the same way he did in the book, only this time, it takes place outside, where they are more visible.)
After the palace basically fell and revealed the two fighting Riders, the battle pretty much ended. The Varden used moment of surprise to gain much needed advantage, and the remaining soldiers just gave up or ran as fast and far as they could.
Thorn and Murtagh lay, defeated but not dead, and Saphira had to fend foe herself with Shruikan. The old dragon was too huge to move fast, but the size allowed him to hurt Saphira in a way she'd never be able to fend off without help. And yet.
With an enormous amount of strength, she pulled at his jaw and snapped it off. Shruikan roared, which sounded rather strange now, and went after her. It was fast, a d unexpected how he struck her in the side, yet she still managed to sink her talons deep in his chest, piercing his heart. He fell partially on her, dead almost immediately, and caused serious injuries to her right side.
Galbatorix felt the death of his dragon, and Eragon used that moment to make his magic even more powerful. He no longer wanted to kill the king. He just wanted to make him see. All the pain he caused. All the bad he's done, or that had been done in his name. The torn families. Burnt homes. Hopeless decades.
Magic no longer flew from him, it just passed through him, like he was a simple medium of communication. All the energy was slowly quenching the king's life, as well as the loss of his dragon had, and he knew death was inevitable.
Nobody could tell how he did it, what spell he used. Not even the most skilled magicians could fanthom what happened next, but with a quiet murmur and a snap of his fingers, Galbatorix slain Eragon and Saphira both, just as he fell dead himself.
Eerie quiet fell upon the field of warriors. No one even though of celebrating the tyrant's death, looking at the defeated Rider a few feet away from him.
Eragon looked even less natural than usually, his skin slowly loosing colour. His features were only more prominent, showing he wasn't a human, and he wasn't an elf. All in all, he looked out of place, but undeniably fragile. Saphira, for all her size, looked incredibly vulnerable all of a sudden. Nothing about them looked right anymore.
All were quiet, tears slowly gathering in the eyes of those who knew him. Just as Roran sank to him knees, a shrill, unnatural cry resounded from somewhere behind, lasting for seconds and stretching thinner and thinner.
A black figure dashed to Eragon's side and Horst, who was close, was ready to ward off whatever being that decides to dishonest the poor boy's body, until he recognized the figure as Arya, the elven ambassador. He shrunk his steps with surprise.
She screamed again, this time, the word being one of the few he managed to learn from the ancient language, a long, painful "no!". She fell to her knees and gripped Eragon's face in her hands, pressing their foreheads together and letting her tears fall over his cold face. Cries of pain continued to escape from her mouth.
Two more elves dashed to her side, placing their hands over her mouth and arms, to prevent her from casting a spell, but it was futile, she threw them off immediately.
And then, into the quiet, she started to sing. It was an uneven melody, and although it was in ancient language, everybody could detect the deafening amount of sadness and pain Arya possessed, paired with love that was fruitless now. The elves who understood the words kneeled down around her and Saphira, joining her mournful melody, soon followed by Angela.
No one moved for hours, listening to the elves. No eye remained dry, as all, friends and enemies, mourned the death of the Rider and his dragon.
Even after all the voices stopped, and Roran with some of the villagers carried Eragon's body away, followed by a never-ending line of people that mourned, Arya remained.
She kneeled in the pool of her endless tears, wailing her broken hearted melody into the distance, so anybody who heard would know her immense pain.

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Words of the Night
FanfictionStuff that I imagine could have been said or done throughout the series, mostly concerning the relationship between Arya and Eragon, and the Carvahall villagers' view of it.