A: Thanks for this interesting question...
I am going to cite the entire passage that you quoted:
(112:3.2) 1. Spiritual (soul) death. If and when mortal man has finally rejected survival, when he has been pronounced spiritually insolvent, morontially bankrupt, in the conjoint opinion of the Adjuster and the surviving seraphim, when such co-ordinate advice has been recorded on Uversa, and after the Censors and their reflective associates have verified these findings, thereupon do the rulers of Orvonton order the immediate release of the indwelling Monitor. But this release of the Adjuster in no way affects the duties of the personal or group seraphim concerned with that Adjuster-abandoned individual. This kind of death is final in its significance irrespective of the temporary continuation of the living energies of the physical and mind mechanisms. From the cosmic standpoint the mortal is already dead; the continuing life merely indicates the persistence of the material momentum of cosmic energies.
To answer your question briefly—the answer is yes. According to this passage, spiritual death means the final destruction of the soul. In such a case, the soul of that person no longer possesses immortality, because it has died, but "the continuing life merely indicates the persistence of the material momentum of cosmic energies." At natural death, the personality will also (presumably) be extinguished.
Now, it is likely that there is still something of value that remains—perhaps some soul-growth that took place before this final determination of soul-death. Such values are indeed immortal and they do survive. In such a case, it would seem safe to assume that that value, as well as the personality of that person, will be added to the "oversoul of creation," or it will survive in the Adjuster, as explained here:
The soul gains immortality due to the freewill decisions of the possessor of that soul. When a person consistently fails to make such decisions, and instead embraces iniquity (the extremity of sin), their soul ceases to grow and no longer has immortal status. You may recall that consistent iniquity indicates "vanishing personality control," and loss of reality.
(2:3.4) ...When the continued embrace of sin by the associated mind culminates in complete self-identification with iniquity, then upon the cessation of life, upon cosmic dissolution, such an isolated personality is absorbed into the oversoul of creation, becoming a part of the evolving experience of the Supreme Being. Never again does it appear as a personality; its identity becomes as though it had never been. In the case of an Adjuster-indwelt personality, the experiential spirit values survive in the reality of the continuing Adjuster.
Our soul is a spiritual counterpart of our physical beings—a spiritual counterpart which grows throughout a lifetime as a result of freewill decisions made and choices made which are in harmony with God's will. It all comes down to freewill choice. When a person decides to reject survival, when "he has been pronounced spiritually insolvent, morontially bankrupt," his soul has ceased to grow. Once the Adjuster takes leave of that person, that person is, in effect, already spiritually dead. They still possess mortal life, however...
This seems a very harsh—and strange—set of events, and hopefully, not something that occurs very often. It is difficult to imagine going through life without the guidance of the Adjuster, and having no soul, isn't it? However, just its mention in the book means to me that it DOES happen. In my opinion, this would have to be a person who knows full well what they are doing—someone who knows and who has experienced God, and then consistently, willingly, knowingly and deliberately decides to reject him and his plan of survival while still on this earth. Again, it seems a very radical decision to make, and I can't begin to judge whether any person is now living with such a fate.
Larger minds than ours make such determinations, and we have to just keep on with our spiritual lives, staying close to God and trying as best we can to grow our souls with consistent decisions towards grace, faith, trust and love—producing the fruits of the Spirit in our lives, and believing through faith that immortality is ours—not by chance, but by choice.
Again, thanks for this interesting question. I hope that my answer has been of some help to you. For a better understanding, you may enjoy having a look at our topical study on the soul HERE ."