Sam's final journey

[Raynor]

If Sam had gone (and I believe JRRT left that one deliberately open) no doubt the same fate was in store for him, and part of the healing would have been a release from his "dependency" on his Master.

If we consider the letters:

Originally Posted by Letter #154

But in this story it is supposed that there may be certain rare exceptions or accommodations (legitimately supposed? there always seem to be exceptions); and so certain 'mortals', who have played some great part in Elvish affairs, may pass with the Elves to Elvenhome. Thus Frodo (by the express gift of Arwen) and Bilbo, and eventually Sam (as adumbrated by Frodo); and as a unique exception Gimli the Dwarf, as friend of Legolas and 'servant' of Galadriel.

Edit:

What about the Avari? They haven't ever been over the sea, nor are they bound to fade like other elves. What happens to them, as they don't want to go over to Valinor? Do they just spend out the rest of their long lives until they die in tragic accidents? Does that mean that there are theoretically some around today ?

The avari too are meant to fade away, due to the: burning of the hroa by the fea; the marring of Melkor. IIRC from Quendi and Eldar, their bodies would fade and they would become "ghosts", visible at will to human eyes.