Word for a conspiracy/cabal/syndicate/etc in which a proper subset of actors are unaware of their roles

The answer is in the question: a sting.

In law enforcement, a sting operation is a deceptive operation designed to catch a person committing a crime. A typical sting will have a law-enforcement officer or cooperative member of the public play a role as criminal partner or potential victim and go along with a suspect's actions to gather evidence of the suspect's wrongdoing.

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The term "sting" was popularized by the 1973 Robert Redford and Paul Newman movie The Sting, although the film is not about a police operation: it features two grifters and their attempts to con a mob boss out of a large sum of money. –Sting operation, Wiki

'A sting' implies at least one party that is not a willing participant. Conspirators, cabals, syndicates and law enforcement all use stings.

Another word is them. As with any group, there's us and them; you're either in or you're out. If you're out, you're not privy.

In closing, allow me to state that any proper conspiracy/cabal/syndicate/etc will have people that are unaware of their roles (and that this distinction is unnecessary; it's intrinsic). Members are often unaware of (or disregard) the hierarchy within their own sect: (honor among thieves, there is not)

No, no, no... I kill the bus driver. –The Dark Knight

The policeman in The Sting who was duped is a patsy.

patsy pat·sy /ˈpatsē/ noun, North American, informal –Google

a person who is easily taken advantage of, especially by being cheated or blamed for something.

Dictionary.com offers the word sucker.