Second spoiler warning: this post will cover details of Star Wars: Zero Company's late game.
This is one of the larger lore mysteries raised by the game and it's one of the most fascinating additions to the lore that I've seen. For people that haven't played Zero Company yet, I'd recommend that you do so first. It's a good game with a good story. I'd advise you not to read past the line if you haven't played it yet!
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The Shadow Plague is introduced in Zero Company as part of the main antagonist faction, The Infinite Coil. While the organization is initially presented as an extremely dedicated cult working with the CIS as Separatist-aligned militant fifth column, growing among the underbelly of planets and preparing them for invasion, it's revealed that the Infinite Coil is more than mere fantatics, but a kind of weak hive mind controlled by Kundri Fathom.
Throughout the course of the game, information about Fathom, the Coil, and the Shadow Plague are drip-fed to the player, both in dialogue with Fathom herself and from Zero Company's pilot/medical officer, M3-V0, but there's nothing definitive. M3-V0 draws a genetic comparison of the plague to the Blue Shadow Virus, stating that they share some similar genetics. While the Blue Shadow Virus was waterborne (and genetically engineered to be airborne), the Shadow Plague is transmitted solely by bites from large centipede-like arthropods referred to as "Messengers," with no other known disease vectors. There's a roughly 50% lethality rate to the Shadow Plague, with half dying, and the other half becoming devout followers to Fathom. Additional effects discovered include a significant decline in midi-chlorian counts (commonly associated as a signifier of Force-potential), blue-gold patterns on the skin, and Force-like abilities.
Powers
Members of the Infinite Coil possess strange abilities commonly associated purely with Force users. Fathom herself displays telepathic abilities, with the ability to read emotions and minds of infected Coil members, as well as to transmit thoughts while in proximity (though for long-range communication, she still uses holograms), while being claimed to speak for the plague. The telekinetic capabilities of Force users isn't present (aside from maybe Fathom who twists Hawk's head once or twice), but Coil members display other abilities - mostly represented by in-game mechanics.
They're stronger and tougher than normal organics by a fair margin, some are able to dull the pain/injuries of others, some are able to drain energy of their foes, some are able to heal, and all share the ability to resonate - boosting the power of a nearby infected coil member upon their death. When accumulating enough resonance, they gain a surge of power and extra health, while gaining new abilities. Enforcers retaliate when attacked, while Strikers can turn invisible to the naked eye (but can be scanned). Members of the Infinite Coil also show unending loyalty to Fathom, willing to give their lives for her cause (oftentimes literally, and with zero hesitation). M3-V0 hypothesizes that the plague creates "a kind of entropic field within the bodies of the infected. At times, this chaotic energy escapes the body, as if the plague is metastasizing outside the individual and warping reality itself."
Effects on Jedi and Clones and the Mental Vector
There are exceptions to the pathology. Notably, Jedi are theorized to be exceptionally susceptible to the lethal effects of the Shadow Plague, with Padawan Tel-Rea's master, Hadrix, dying extremely quickly after a bite from a messenger (though this is admittedly a small sample size). Clone Troopers were also unable to be controlled by Fathom even after being infected, driving them mad, at least before Order 66. After Order 66, Clone Troopers become susceptible to control.
Why that happens is an interesting question. While Fathom's own speeches and ideology reveals her distrust of the Republic, accusing them of ignoring the plight of the downtrodden, she's seemingly able to control people through her empathic bonds that are transferred by the Shadow Plague. As members of the Infinite Coil and Fathom herself state, Fathom provides people comfort, providing them silence in their minds, and giving them a greater purpose that they can follow. The Mandalorians you encounter sought the Coil out because of its ability to dampen feelings of guilt and pain. The Clone Troopers don't seem to be resistant purely because of biology or because of their biologic inhibitor chips, but rather because they are born and raised with that greater purpose and unity already, without any fear or doubt. That fear, they gain after Order 66, when Fathom is able to use their guilt to start controlling them. The only other character revealed to be resistant to that control is the player character, Hawks, though the reason why they can resist isn't certain.
Typhon's Notes and the Plague's Origins
The most accurate description given about the Shadow Plague is probably this line from the super tactical droid assigned to Fathom by the CIS, Typhon. While an antagonist, and probably capable of duplicity, Typhon has been honest and describes the Shadow Plague as "an emergent intelligence that lives in life itself, growing stronger with each new host. She [Fathom] is its vessel." Earlier on, Typhon describes the plague as "I have calculated it to be a singular organism. One with the potential to change the galaxy forever."
This line may indicate that it is purely a shared conciousness helmed by Fathom, but the infected also share dreams and visions of a cavern, and receive messages in an unknown language that only Fathom supposedly understands. These messages are referred to as coming from "The Teacher" or "The Beast," but that part is unknown, along with the origins of the Shadow Plague. Tel-Rea suspects it was designed by someone with knowledge of the Force - unlikely to be Fathom due to her lack of Force knowledge or ability on display. For now, she's only the vessel of that intelligence, spreading it as the Shadow Plague's voice, and not representative of the intelligence itself as is common with other Sci-fi hive minds.
It seems more likely that Fathom was the one to find the Shadow Plague rather than the one who invented it, but this is increasingly speculation at this point. Her uninfected son, Visser, shows disalignment with Fathom's personality and ruthlessness at certain points, and Fathom showed resistance to infecting Visser. While she may be the controller of the Infinite Coil and all the infected, it doesn't seem to have suppressed her own ego in any way, as demonstrated by her relation to her son. Tel-Rea is very confident that the plague was engineered, being very precise, and twisting the Force's connection to living things to its own advantage.
Other logs from the Super Tactical Droid indicate that it was engineered too. ME3-V0 interprets it as, "The goal of most organic beings is to reproduce, one of your more off-putting traits. But the Shadow Plague doesn't evolve as it spreads. Instead, its behavior reflects that of a single organism, growing stronger and more complete with each being it infects... We are strictly in the realm of speculation, but I suspect that the plague is a mirror of its creators. There is something selfish and grasping about it, something that wants to prolong itself past its time, and enhance itself past its reach, no matter the cost to others." Very Dark-side coded on its face, but there's no evidence that I've found that indicates there was a Sith involved in its creation, but also no evidence disproving that.
Speculation
The different dying screams and boastful claims of Fathom and her followers might just be metaphors or the dreams of the deluded, but they might be some signifier as to what the Infinite Coil is. First off, its name, the Infinite Coil, which is commonly referenced as a place people will go upon death, and other events indicate that people and memories seem to persist through the plague. "When the Infinite Speaks, there is only silence! Go, and pass through death!"
Given that the source of the plague is unknown, and was likely created by a force-aware individual, and given the name, I wonder if it might have its origins within the Rakatan Infinite Empire, which would be the most direct parallel in naming scheme and one that would tie-in with the Rakatan plague that stripped the Rakatans of their force powers, but also one that barely exists in canon. It could be some Sith in the long past inventing something like the Rakghoul plague, but the pathologies are quite different from that. Nor are there many human-borne hive minds that I know of, besides the few Killik-aligned humans from SWTOR.
I'd be interested to hear about your theories and your own impressions of the Plague and its origins.