Unicorns are immortal. It is their nature to live alone in one place: usually a forest where there is a pool clear enough for them to see themselves -- for they are a little vain, knowing themselves to be the most beautiful.
"He would have liked his own funeral if he could have seen it. It was small and quiet, and really not at all pompous, as Michael had feared it might be. 'The dead,' he had said once, 'need nothing from the living, and the living can give nothing to the dead.' At 22, it had sounded precocious; at 34, it sounded mature, and this pleased Michael very much. Essentially a romantic, he had put away the trappings of romance, although he had loved them deeply and never known."
"For in the end it is Middle-Earth and its dwellers that we love, not Tolkien's considerable gifts in showing it to us. I said once that the world he charts was there long before him, and I still believe it. He is a great enough magician to tap our most common nightmares, daydreams and twilight fancies, but he never invented them either: he found them a place to live, a green alternative to each day's madness here in a poisoned world. We are raised to honor all the wrong explorers and discoverers - thieves planting flags, murderers carrying crosses. Let us at last praise the colonizers of dreams."