If one takes JRRT's comment (from a letter, IIRC) that the beginning of the
Fourth Age was about 6,000 years ago, and then adds to that some murkiness about how
Saruman bred the (his?)
Uruk-hai, plus some of the people fleeing from the south to
Bree being described as half-Orcs ... (ask S-eS

)
It would seem to me that no more "pure-bred"
Orcs exist anymore. And however it was achieved, and by whom, to breed them "pure", it must have been from human stock. "Historical" records start about 1,000 years after the fall of
Barad-dûr, by this hypothesis. By this time the "pure-bred" Orcs had been reabsorbed into the mainstream of human stock, as there is no dearth, more precisely no end of
Orcish behavior recorded in those historical records.
This is a fairly significant misreading of
Tolkien’s statements regarding the connection of
Middle-earth to our Earth.
Middle-earth isn’t anything, or anywhere in our Earth’s past.
It exists in a
possible past.
The works of Boethius, I believe his
Theological Tractates and Consolation of Philosophy, contain the relevant material on the issue of Sub-Creation as it relates to Tolkien’s Middle-earth, which will better explain how Tolkien thought of Middle-earth simultaneously as a very real place that exists “in a possible past” of this world, while at the same time being a work of Mythological Fiction, referring to a “place of the imagination.” This is a very Catholic view of something that contains a paradox, very much like the Catholic conception of a Trinity. But it addresses the issue of the “possible past” quite thoroughly.
As Tolkien points out in
Letters,
No. 153 to Peter Hastings, Middle-earth is indeed a separate world, which had different features of Physics, Chemistry, Biology, and so-on, than does our world. Meaning that while he states elsewhere in
Letters that Middle-earth is AKIN to a supposed past of “our Earth.”
The Letters of JRR Tolkien said:
This is a biological dictum in my imaginary world. It is only (as yet) an incompletely imagined world, a rudimentary ‘secondary’; but if it pleased the Creator to give it (in a corrected form) Reality on any plane, then you would just have to enter it and begin studying its different biology, that is all.
So... Tolkien here points out that Middle-earth is a
purely imaginary world, distinct from our own, else one would not need “just have to enter it, and begin studying it[s different biology]...” If Middle-earth was indeed our Earth, then the “
biological dictum” Tolkien is discussing here in this letter (which concerns Michael Hastings’ inquiries regarding the
biological immortality of
Elves, their Reincarnation, and how Humans and Elves breed, and the fate of their children) could be resolved by simply studying the biology of the inhabitants of our world, where the genetic lineage of the Elves would remain within the offspring of the 2 Unions of Elves and
Men (3, technically), which would be a quite substantial population by now.
This is something we are able to currently do in Biology (trace the Genetic Lineage of people back to specific ancestors for whom we have viable DNA samples. The discovery of the “Mitochondrial Eve” in Africa is just one specific example), and DNA would exist that revealed such properties. There are a great many other things betraying our Earth as being “Middle-earth,” and why attempts to connect the two are doomed to failure.
The quote you may be remembering from
Letters is from
Letter No. 165, responding to an inquiry a fan made to the Publisher regarding Middle-earth, where Tolkien says at one point during his response:
The Letters of JRR Tolkien. No. 165 said:
... imaginatively this ‘history’ is supposed to take place in a period of the actual Old World of this planet.
However, in many other
places in the remaining sources, not the least of which are other letters in
Letters, Tolkien makes it very clear that Middle-earth exists
no-where in our ACTUAL PAST. Middle-earth represents a “possible past,” in the same way that all Mythology represents a “possible past.”
If one goes back to the sources, whether of fiction, or Theological, Philosophical, Metaphysical, or Academic, and becomes familiar with these (Plato, Aristotle, Boethius, Augustine, Origen, Beowulf, Gothic and Saxon History, the Norse Eddas, William Morris — From whose world Tolkien
heavily borrowed — and other works of Chivalric Romance), and then returns to the Primary and Secondary Sources of Tolkien himself, these works then reveal a vast deal of influence and connection to Middle-earth, and many things that previously seemed to be “deeply mysterious” will suddenly become clear as day (like
Tom Bombadil, just as one example).
As to the points about “Pure-Bred Orcs,” this again is contingent upon “What is an
Orc?”
As is the comments regarding “Half-Orcs.” The comments on that don’t actually say “That is a “Half-Orc,” and this one is “Pure-Bred” for an Orc.” Usually the reference is something along the lines of “He appears to be more than half an Orc,” or something of the sort.
One would first need to resolve what an “Orc” actually is before one can begin any claims about “Pure-Bred,” a term that is
especially fraught given that it arises from only two sources,
both hugely suspect in terms of being anything real in Biological Terms.
”Pure-Bred” has its origins in the breeding of
animals, and even here it is highly questionable in terms of “What genes are “pure” to begin with?”
Which brings us to the second source of “Pure-Breed/Bred:” White Nationalists/Supremacists, Nazis, and Fascists.
While “
Race” is something that seems to “Actually Exist” within Middle-earth, it isn’t something that exists in our World.
And, as such, one would need to provide a definition for “Pure-Bred/Breed” to begin with, given that even in domains where such a term has a relevance (Dog and Cat Shows, The Breeding of Cattle and
Horses/Thoroughbreds, and so on) it remains something that is nigh impossible to define save in terms of appearance (What is known as “Phenotype” in Biology).
And in Biology, we have discovered that what
appear to be
identical Phenotypes can arise from
categorically different Genotypes (different “Genes,” meaning that the term “Pure-Bred” becomes even harder to define).
This is a subject I have put a lot of time in toward an attempt to resolve or make any sense out of (much as the existence of “Free-Will,” another thing that turns out to be nearly impossible to define in any way that actually means anything) given that “Race” in Middle-earth is an
Actual Thing.
Dwarves, Elves, Orcs, Humans (including
Hobbit),
Ents,
Trolls, ... These things seem to be “Actual
Races” in the terms that this word has come to usually mean... But There needs to be a “Thing,” re:
Some-Thing as opposed to
No-Thing, that provides a means to determine ”Racial Membership” within Middle-earth... And lacking the means to “enter it and begin studying” it, the ability to discover that “thing” is elusive and complicated in locating.
MB