There was a path left to the West for the Eldar who wished to return for they were all welcome. The Valar probably requested that the ring bearers that were left alive be brought since they had lived in the world of the wraiths for small periods of time.
The reason that they could live forever in the West is because it is a different kind of environment than the rest of the world. Middle-earth is in a layer of air called Vista. The next layer of air is called Ilmen .the western and eastern bits of land (Valinor and the Lands of the Sun) extend into this layer of air. The next layer is called Vaiya. This is the Outer Ocean where Ulmo dwells (it is a thinner type of water than the inner oceans). Beyond that is Kuma. That is the Outer Void where Melkor is kept until the end.
The air in Ilmen may have something to do with keeping beings alive. The Quenya and Maia and Vala can live forever no matter what because they are bound to the earth until the end. Even if any of these are killed their souls live on (like Sauron’s did a few times) and can’t be killed completely. The Quenya are reborn in their children so they keep living also.
It is not known where men go. They leave the world and only Illuvator knows what is their fate. This is their gift.