For jargon, I think the mafia term "cult" works fine.
A cult is any type of recruiting organization who's existence is kept secret from other parts of the society.
Cults could be good (a secret order of noble defenders), neutral (a secret cult devoted to selling girl scout cookies) or evil (a secret group of demon worshiping traitors).
So the question is: how would a cult form? What would determine it's purpose? (i.e. what would cause a good cult to form vs. an evil cult). What would the cult do? (nothing is acceptable in some cases, but for traitors you'd expect them to start opening doors for defenders or something). How would it recruit? Could it evolve?
I'm thinking that cults would form from a variety of reasons:
Evil:
1) Demon possession, especially in evil environments
2) Enemy civs. An "immigrant" is really a spy & sabateur
3) Excess misery could cause revolutionaires
Neutral:
1) Common Interests
2) Religion
3) Profession (secret guild of crafters or metalworkers?)
Positive:
1) Heroics (a champion forms a small squad of citizens to secretly train them into a mighty militia
2) Excessive happiness (might form a sort of neighborhood watch organization to protect the peace.)
3) Fey posession (if in a good region)
Purpose would be random + combo of their formation. But here's a list of what I think some sample "purposes" might be
1. Kill nobles (e.g. revolutionaries might want to kill the hammerer for beating them up!)
2. Overthrow kingdom (Demons & revolutionaries & sabateurs might want to get themselves elected
3. Spread religion/interests/items (Mostly for the neutrals. religion for demon worshippers, interests for the cult of things that are blue, items for the crafter's guild)
4. Defend the kingdom (for the good ones).
5. Perform a magic ritual (think of this as artifact creation for a group. Instead of one dwarf running around you have a bunch of dwraves running around nad gathering items. If it's a good ritual you might let it happen, even encourage it. If it's a ritual to open a portal to HFS in the middle of your fort, you'll rush to try and reroute the magma in time.
6. Gather wealth
So how would the cult accomplish these goals?
1. It would recruit and remain secret until it has enough numbers or military skills to bypass royal guards and kill the noble in question. The cult would reveal itself, grab weapons & armor and make a beeline towards the noble in question. They'd be treated like beserking dwarves, so other citizens might run away or stand up and try and stop them (depending on overall opinion of said player and player direction). Military that isn't cult would try and stop them. This continues until either the cult is wiped out or the noble is dead. If the noble dies, the cult can either dissolve (if they're still dwarfy at heart) or continue the carnage (for evil cults).
2. Like the above, but the culty dwarves would be flagged as hostiles permanently. So if they wipe out your fortress, game over.
3. They would recruit to a point, but otherwise would talk to people and slowly shift their interests towards the cult's stuff. They might also get into a fight with people who hate their object. So a person neutral towards blue things starts talking to members of the cult of blue things, and if he develops a positive relationship with those culties, he slowly starts liking, then loving blue things. Eventually he might even join the cult! If he hates blue things though, they might get into a fight that would have to be broken up by authorities.
4. Champion takes time out from patrols to try and recruit people. People recruited would secretly train in the barracks while they're on break. That way when all hell breaks loose and the kingdom is invaded, suddenly the player discovers that a group of farmers and brewers are decent level swordsmen! (actual weapon woudl be based on champion's preference. Player wouldn't be able to dictate (except he can always draft these skilled dwarves into the army). The unit stats screen would just show the dwarves as being "ON Break" and not "Picking up equipment" "sparring" etc.
5. Cult grows to a certain size and then moves to gather items into a particular workshop. The leader will claim the workshop and the other culties will run around grabbing items. The cult will be revealed at this point and so the player won't be able to control the cult dwarves. Once all the items are gathered, cult leader begins "constructing" but the end result is

When magic is put in, a magic effect could happen, using existing mechanics could do stuff like create an artifact or trigger a bunch of demons that slaughter the cultists and then go to town on your fort.
6. This is an abstract one. I just envision once the economy is turned on a group of dwarves that try and manipulate things to control the economy. I'm not to familiar with the economy system so how they'd do this is a mystery to me...
How do cults recruit? I'd say by talking to people. As they build relationships, they'll bring people in line with their thoughts. I think this should be an exponential growth in difficulty though to preven tcults from growing out of control.
For example, the first recruit only takes a "day" of time to recruit, the second "two days" etc. The fifth or so might take a full season to develop, while the 10th recruit might take a full year to develop. Cults would build up over the years and then trigger depending on their purpose. I think at least 10 dwarves are needed before a cult will trigger though...
Secrecy? the player should not know a cult exists before it triggers (if it ever does) and should only know who the cult leader is through careful observation. There are some exceptions though.
Take this example scenario:
Urist McTraitor becomes possessed by a demon to start up a cult to try and kill the king. He is subtle though, going about his business as usual. However, when he's on break he makes a beeline towards friends & family to convince them with his devilish silver tongue that the king is unjust. The player just sees Urist chatting to his best friend, nothing wrong with that. As the cult grows larger though, the player may (but probably not) realize that Urist is taking longer and longer breaks, even when he's on military duty and is specifically talking to the same people over and over again (again, probably not noticable in a large 80 dwarf fort, but an astute player might see it happening). To the non-observant player it just looks like Urist is being another dwarf.
Once the cult grows sizable, plans are made. Operatives start taking weapons from the stockpiles and stashing them in their chests. Again, an observant player might wonder "why does Urist have a dagger in his chest" but perhaps if a future improvement allows dwarves to "hide" items from the player, the player might just realize "hey, why are some weapons missing?" and be unable to locate them on the stock screen or anywhere. An observant player might watch the armory to see what is happening, but again that's if they even realize what's going on.
Finally, the time is ripe to strike. One of the royal guards has been turned. Urist makes one last visit to the other dozen cult members and tells them to prepare to strike at X;XX time. At around that time, suddenly all those dwarves go on break. Again, a player who suspects a cult is happening might start mustering up the guard in anticipation but otherwise nothing too unusual. The dwarves run back to their rooms and don weapons & armor. An announcement is made:
"Urist McTraitor has declared that King Urist McKingsley must die in the name of the demon Urist McDemon! The Cult of [RANDOM NAME] has revealed themselves!"
The cult members start running towards the king's bedroom. The royal guard arrange themselves to protect him but are betrayed as one of their own turns hostile. Battles erupt all over the fort as cult members stab at anyone in their way. The traitor royal guard kills his squad mates and rushes into the king's bedroom. The king screams and flees, but the traitor guard catches him! The guard shoves his bloody sword through the kings chest, screaming victory for the Demon McDemon!
Urist McTraitor, his mission accomplished, immediately starts to flee the kingdom. A heroic champion catches up to him though and smashes his head in with a hammer. The assembled military quickly dispatches the remaining dwarven cult members, who were still madly trying to further McDemon's cause with the blood of the innocent.
All in all, a dozen dwarven cult members, some of them legendary crafters lie dead. The royal guard is in shambles and the whole kingdom is rocked by news of the death of their king...