Origin of species (at least the hobbits)

[Carnimírië]

Hobbits are a sub-group of humans, that is hinted at in the Prologue and made clear beyond question in Letters.

It is plain indeed that in spite of later estrangement Hobbits are relatives if ours: far nearer to us than Elves, or even than Dwarves. Of old they spoke the languages of Men, after their own fashion, and liked and disliked much of the same things as Men did. But what exactly our relationship is can no longer be discovered. The beginning of Hobbits lies far back in the Elder Days that are now lost and forgotten.

LotR Prologue

Letter 158 makes it clear:

The Hobbits are, of course, really meant to be a branch of the specifically human race (not Elves or Dwarves) -- hence the two kinds can dwell together (as at Bree), and are called just the Big Folk and Little Folk. They are entirely without non-human powers, but are represented as being more in touch with 'nature' (the soil and other living things, plants and animals), and abnormally, for humans, free from ambition or greed of wealth.

Therefore hobbits have the same fate after death as Men.