### The Elves who stayed in Middle-earth became wraiths (perhaps) ###
In _The Silmarillion_, Elves are said to have become "shadows and memories":

> In after days, when because of the triumph of Morgoth Elves and Men became estranged, as be most wished, those of the Elven-race that lived still in Middle-earth waned and faded, and Men usurped the sunlight. Then the Quendi wandered in the lonely places of the great lands and the isles, and took to the moonlight and the starlight, and to the woods and caves, **becoming as shadows and memories**, save those who ever and anon set sail into the West and vanished from Middle-earth. 

> <sup>_The Silmarillion_, Of Men, p. 117</sup>

However, in an earlier version of this text, the Elves were said to become wraiths:

> In after days, when because of the triumph of Morgoth Elves and Men became estranged, as he most wished, those of the Eldalie that still lived in the world faded, and Men usurped the sunlight. Then the Eldar wandered in the lonelier places of the Outer Lands, and took to the moonlight and to the starlight, and to the woods and caves, and **became as shadows, wraiths and memories**, such as set not sail unto the West and vanished from the world.

Why Tolkien decided to remove "wraiths" from the text is unknown to me, so take this with a grain of salt. It as also says "became _as_", so it might be a figure of speech.

### Seeing unhoused _feä_ ###
A "ghost" on Arda would be a _feä_ ("soul") without a _hroä_ ("body"). Normally, unhoused _feär_ are not just roaming around. In the case of an Elf, it would be in the Halls of Mandos. It is unknown where the _feä_ of Men goes.

However, Finrod does talk about seeing a _feä_ in a discussion with Andreth:

> 'Men say various things, be they Wise or no,' said Andreth. 'Many hold that there is but a single thing: the body, and that we are one of the beasts, though the latest come and the most cunning. But others hold that the body is not all, but contains some other thing. For often we speak of the body as a "house", or as "raiment", and that implies an indwelling, though of what we speak in uncertainty.

> 'Among my folk men speak mostly of the "breath" (or the "breath of life" ), and they say that if it leaves the house, it may by seeing eyes be seen as a wraith, a shadowy image of the living thing that was.'

> 'That is but a guess,' said Finrod, 'and long ago we said things similar, but we know now that the Indweller is not "breath" (which the _hroä_ uses), and that seeing eyes cannot see one that is houseless, but that the living eyes may draw from the _feä_ within an image which the houseless conveys to the housed: the memory of itself.'

So it appears you can't normally see an unhoused _feä_ unless it conveys an image of itself to you. However, I haven't found an example of someone seeing an unhoused _feä_ in any of the texts.