Okay. The dilemma has been pretty well stated by Prim and Sassy.
On the one hand, like Prim I believe that it is absolutely imperative that the Orcs do not have redeemable souls. I believe the whole moral structure of LOTR and indeed all of Tolkien's work collapses like a house of cards if they did.
On the other hand, as Sassy demonstrates, the only possible conclusion that one can reach from the full body of Tolkien's work is that the Orcs came from beings that did have souls (fëa), possibly men but also undoubtedly including Elves corrupted and twisted by Melkor (and even possibly some Maian spirits, which she doesn't mention).
How then can these two seemingly contradictory points be reconciled? The answer comes from a surprising source.
But before I go there I wanted to make another point. There is some precedent in Tolkien's writing for the idea expressed in Myth's Transformed that despite having speech and even cleverness the Orcs possessed no 'rational soul' or fëa. In the chapter "Of the Coming of the Elves" in the Later Quenta Silmarillion (published in Morgoth's Ring) (in what appears in the second paragraph of chapter three of the published Sil) in talking about the Balrogs the word "(ëalar)" appeared after "These were the" and before the word "spirits" with a footnote explaining that this word did not refer to an incarnate spirit, which was "fëa" and that it simply referred to "being". Thus the Balrogs themselves, as powerful as they were, and even being the first ancient spirits that allied themselves with Morgoth, were seen as merely having "being" and NOT having incarnate souls. I believe the explanation that I point to below must apply to them as well.
Okay, turning back to the paradox described above. How do I explain how the Orcs could not have incarnate souls when they were derived from beings that did have incarnate souls. I find the answer in, of all places, the Athrabeth. As I have discussed before, one of the key concepts discussed in the commentary and notes that follow the Athrabeth is the idea that "the separation of fëa and hröa is 'unnatural', and proceeds not from the original design but from the 'Marring of Arda', which is due to the operations of Melkor." It is from this concept that I derive my answer to the dilemma.
The Orcs originated from the hröar of originally incarnate beings (whether Elves or Men or both, and even as I believe Tolkien suggests at one point in Myths Transformed from some Maian spirits as well) that Melkor managed to separate from their fëar. Like the Balrogs these corrupted beings had "ëalar" or "being" but not "fëar" or souls. They had no wills of their own, but rather were animated by Melkor's own will, and later by Sauron's as Melkor's proxy. They were similar in that way to the beings created by Aulë before Eru took pity on him and them and gave them their own independent wills.
This would even explain why, as Prim, pointed out, the Orcs "magically" died when Sauron was destroyed; with no will of their own there was nothing to animate them once Melkor's proxy was destroyed.
As for Sassy's final quote, I don't see anything there that is an obstacle to this explanation. If these former Elves were mated with Men, it must have been Men who similarly had been stripped of their fëar (and beasts never had fëar in the first place). As for them going to Mandos and held in prison until the End when they died, that sounds like a reasonable precaution to prevent Melkor from re-animating them and causing even more mischief.
As for Saruman breeding Men and Orcs, I don't believe it for a second, and I don't believe that anywhere does it categorically say that he did so; it is only speculation. No, those "half-Orcs" were simply Orcs that Saruman through his dark arts was able to make appear more man-like but still had no fëar of their own.
That's my story, and I'm sticking to it. ;)
Voronwë the Faithful post in this conversation
https://thehalloffire.net/forum/viewtopic.php?t=379&start=20 
