She has many family connections:
While Eärendil was away at sea, the remaining sons of Fëanor descended upon the Havens, killing many Elves. Elwing cast herself into the sea rather than be captured, but Ulmo changed her into a great white bird, in which form she found her husband. Lacking a home to return to, they instead went together west to Aman.
The Valar gave her the choice of kindred just as for her husband and sons, and she elected to be with the Elves and live in the Blessed Realm. But instead of traveling with Eärendil and the Silmaril on his nightly sky-voyages, she lived in a white tower next to the Sundering Seas, conversing with the seabirds and flying among them.