The Silmarils do not burn them.
They do not know why this is shocking. They run. The War is over now, Morgoth banished in the Void and they have two Silmarils (after all this time). The third one is impossible to acquire but it is fine (the Oath is not silent it never is but it is better it is bearable).
Time passes and still they keep moving (Elros is a king and Elrond has no need of them now).
When Elros dies they feel it in their bones. His name is one of many etched upon their souls and they know when he breathes his last just like they know their own names (they let Elrond find them then on a beach).
The world breaks and splinters and Elros' legacy drowns under the rage of a God who abandoned them long ago. (they are not surprised though, the doom of Mandos rings in their ears) (Elrond sends news that the descendants of his brother managed to survive)
The Silmarils do not burn them.
War comes again. Sauron is nearly desperate in his attempt to continue what his master started and he either forgot they were alive or decided to ignore them (he can't ignore them when they charge against him standing tall beside their son, Silmarils upon their brows)
They fight. Sauron has neither Morgoth's power and might nor his army of balrogs and dragons. But he is still a Maia.
They fight and fight and fight besides elves who hate them (with good reason), besides men who flinch from them (even better reasons) but nobody contests that they have been fighting since before the moon and sun existed and so they remain undisturbed.
The Silmarils do not burn them. (but their light burn the orcs and other creatures and gives hope to their comrades)
The War of the Last Alliance ends bitterly. So many elves and men dead in a war that started so long ago even they forgot. Sauron may be gone but his power is still tied to the Ring (lost as it is with Isildur's death). They have been alive for too long and are too jaded to hope that it will stay lost and forgotten. Sauron will rise again and war will come. They just don't know when.
They are in Imladris when Gandalf comes with the dwarves. They are not invited to the White Council (and even if they were they wouldn't have gone they have no wish to impose their presence on Galadriel) but they don't need to be. They know what has started. Maglor doesn't know whether to feel smug that they were right or sad. In the end all he feels is tired. He has lived too long to feel anything else. Maedhros doesn't say anything (it has been a long time since he spoke) but the fire that burned in his eyes after Thangorodrim is still as strong and fiery as the color of his hair.
They leave Imladris the next day. And they wait.
The Silmarils do not burn them and the Oath is nearly silent.
Before they know it (time had stopped having meaning for them millennia ago) the War starts. They return to the world just as Frodo arrives in Imladris. Elrond invites them to his Council. The Ring is plain and Maedhros can nearly hear his father scoff at the inferior workmanship (they cannot be corrupted by it, they have the Silmarils). When Gandalf dares speak the Black Speech Maedhros is the only one who doesn't flinch (after years of hearing it in captivity he has become desensitized to it)
They fight. They win. Elrond sails. They remain. Ages pass and history forgets. They do not fade. They wander the world and wait. War will come again. And they will fight (they know nothing else now)
