"The jewel which Beren had won and Lúthien had worn, and for which Dior the fair was slain." [S]

"The Silmaril rescued from Morgoth by Beren and Lúthien, and given to King Thingol Lúthien's father, had descended to Elwing dtr. of Dior, son of Lúthien." [Letters]

 

"Thus Doriath was destroyed, and never rose again." [S]  

 

Please note the following idea:

"It is a natural assumption that Celeborn and Galadriel were present at the ruin of Doriath (it is said in one place that Celeborn "escaped the sack of Doriath"), and perhaps aided the escape of Elwing to the Havens of Sirion with the Silmaril – but this is nowhere stated" [Christopher Tolkien, UT]

4. The survivors of Doriath were joined on the Mouths of the Sirion by Idril Celebrindal and Tuor, parents of Eärendil Half-Elven.

 

"Idril and Tuor departed from Nan-tathren, and went southwards down the river to the sea" [S]

5. She wedded Eärendil (who by this time was the Lord of the Mouths of the Sirion), and bore him Elrond and Elros, the Peredhil. From Elros would descend all the Kings of Númenor, and the heirs to the throne of Gondor; while Elrond would come to play a major part in the History of the Second and Third Ages.

 

"In the glory and beauty of the Elves, and in their fate, full share had the offspring of elf and mortal, Eärendil, and Elwing, and Elrond their child." [S]

"Of Eärendil came the Kings of Númenor, that is Westernesse." [FotR]

 

Note that, through the joining of Eärendil (son of Man and She-Elf) and Elwing (granddaughter of Beren and Lúthien), the two marriages of Firstborn and Secondborn converge in one family tree.

"The problem of the Half-elven becomes united in one line." [Letters]  

6. Eärendil felt the urge to Sail the Seas, to search for Valinor and for Tuor and Idril; Elwing, Elrond and Elros were left behind, at the Mouths of the Sirion.

 

"She sat in sorrow by the mouths of Sirion." [S]

7. Eärendil, having not reached Valinor nor found his parents, set sail back to the Mouths of the Sirion.

 

"In longing for Elwing he turned homeward towards the coast of Beleriand." [S]

8. The sons of Fëanor still longed to possess the Silmaril. Before Eärendil returned, they attacked the exiles of Gondolin and of Doriath, slaying many of the Elves of Arvernien, but losing many of their own, too. In the end, Maedhros and Maglor were the only sons of Fëanor still standing. 

 

"They sent messages to the Havens of friendship and yet of stern demand. Then Elwing and the people of Sirion would not yield the jewel." [S]

"There came to pass the last and cruellest of the slayings of Elf by Elf." [S]

9. Elwing, to save Lúthien's Silmaril, cast herself into the Sea, carrying the jewel upon her breast. Elrond and Elros were left behind, and taken captive by the sons of Fëanor. The survivors of the siege fled to Balar with the High King Gil-galad, who had sailed with Círdan to Sirion.

 

"Too late the ships of Círdan and Gil-galad the High King came hasting to the aid of the Elves of Sirion; and Elwing was gone, and her sons." [S]

10. Ulmo took pity on Elwing and transformed her into a great white sea bird, still bearing the Silmaril, shining on her breast. In this form she flew over the waves to Vingilot, Eärendil's ship.

 

"On a time of night Eärendil at the helm of his ship saw her come towards him, as a white cloud exceeding swift beneath the moon, as a star over the sea moving in strange course, a pale flame on wings of storm. And it is sung that she fell from the air upon the timbers of Vingilot, in a swoon, nigh unto death for the urgency of her speed, and Eärendil took her to his bosom; but in the morning with marvelling eyes he beheld his wife in her own form beside him with her hair upon his face, and she slept." [S]

11. Eärendil and Elwing sailed once again in search of Valinor and, through the power of the Silmaril, found the way to its shores. Elwing stepped into Aman, though Eärendil had asked her to stay behind so he alone would have to face the wrath of the Valar. 

 

"With the power of the great Gem they pass at last to Valinor, and accomplish their errand – at the cost of never being allowed to return or dwell again with Elves or Men." [Letters]

 

"Here none but myself shall set foot, lest you fall under the wrath of the Valar. But that peril I will take on myself alone, for the sake of the Two Kindreds." [Eärendil, S]

"'All thy perils I will take on myself also.' And she leaped into the white foam and ran towards him." [Elwing, S]

12. Having been left behind while Eärendil addressed the Valar, Elwing "became lonely and afraid". She found her way to the Haven of the Swans [Alqualondë], where she met the Teleri.

 

"The Teleri befriended her, and they listened to her tales of Doriath and Gondolin and the griefs of Beleriand, and they were filled with pity and wonder." [S]

13. The Valar decreed that the descendents of Man and Elf must choose among which race to be counted and judged.

"The peril that he ventured for love of the Two Kindreds shall not fall upon Eärendil, nor shall it fall upon Elwing his wife, who entered into peril for love of him; but they shall not walk again ever among Elves or Men in the Outer Lands. And this is my decree concerning them: to Eärendil and to Elwing, and to their sons, shall be given leave each to choose freely to which kindred their fates shall be joined, and under which kindred they shall be judged." [Manwë, S]

14. The decision of the Valar was transmitted to Elwing and Eärendil, and they had to make their choice - and Elwing chose to be counted among the Elves, like Lúthien. So Eärendil chose likewise. Their son Elrond, too, would decide to be judged as a Firstborn, but Elros opted for Mortality, and became the first King of Númenor.

15. Eärendil forever continued sailing his ship through the Seas and the Heavens. Elwing stayed behind in a White Tower on the margin of the Sundering Seas, in the company of sea-birds, flying to Eärendil with wings of white and silver-grey whenever he sailed near Arda.

"On those journeys Elwing did not go, for she might not endure the cold and the pathless voids, and she loved rather the earth and the sweet winds that blow on sea and hill."

"Elwing learned the tongues of birds, who herself had once worn their shape; and they taught her the craft of flight."

"When Eärendil returning drew near again to Arda, she would fly to meet him, even as she had flown long ago, when she was rescued from the sea. Then the far-sighted among the Elves that dwelt in the Lonely Isle would see her like a white bird, shining, rose-stained in the sunset, as she soared in joy to greet the coming of Vingilot to haven." [S]