There at last when the mallorn leaves were falling, but spring had not yet come, she laid herself to rest upon Cerin Amroth; and there is her green grave, until the world is changed, and all the days of her life are utterly forgotten by men that come after, and elanor and niphredil bloom no more east of the Sea. Lord of the Rings, Appendix A, p.1038
The winter had come. The leaves of the mallorn were falling, and the land of Lorien was reaching the end of the glory it once had known.
And Arwen Evenstar, once Queen of Gondor, knew that her time had come.
As she walked through the forest for the last time, it seemed to her that she heard an echo of the joyful singing that had filled that realm in former times. But the Lord and Lady of that place were gone, and all their subjects with them, leaving the Golden Wood empty and cold. She shuddered at the sight of the once-beautiful trees, bare now and angular like skeletons.
Arwen had chosen her path long before, and had cleaved to it through all grief, until the choice was no longer hers to make. Only on the departure of her brothers from Middle Earth had she seen the dead end that lay before her, as it lay before all those born to the Doom of Men. Only then had she understood that her fate, like theirs, was the loss and the silence.
Well, the loss she knew, and the silence was upon her now. It was near impossible to bear, to see what had become of the home she had once known. And yet, she had always known this was inevitable. She journeyed now to Cerin Amroth where she would make her final resting-place.
When she reached the summit of the hill, she picked the greatest of the trees growing there, and made her grave in the hollow of a great root. As she knelt beside the place, she spoke into the silence, to those who would never hear her words.
"I bid you farewell, my father, my mother, my brothers. I go now to meet my husband in Mandos' Halls, and we will not be reunited, you and I. I wish you well beyond the ending of the world. Goodbye."
She laid herself down and closed her eyes. And the last of the Elven-born passed out of Middle-Earth forever.