There is a phrase for someone assigned to do that or similar deeds: agent provocateur.
An agent provocateur (French for "inciting agent") is a person who commits, or who acts to entice another person to commit an illegal or rash act or falsely implicate them in partaking in an illegal act. An agent provocateur may be acting out of their own sense of duty or may be employed by the police or other entity to discredit or harm another group (such as a peaceful protest or demonstration) by provoking them to commit a crime, thereby undermining the protest or demonstration as a whole.
In accordance with French grammar, the plural form of the term is, agents provocateurs; a female agent is an agente provocatrice.
To prevent infiltration by agents provocateurs, the organizers of large or controversial assemblies may deploy and coordinate demonstration marshals, also called stewards.
—Agent provocateur, Wikipedia
The article lists examples from the 19th, 20th, and 21st centuries.
There is a legal term for when undercover agents of the police get someone to agree to or actually commit a crime they otherwise would not have done: entrapment.
And I have read a number of accounts of ancient and medieval events in which it was claimed that agents provocateurs pretended to be someone's friends and provoked them into saying or doing something that would get them executed.
So it would not be totally unlikely for government agents provocateurs to start a revolt against their government if they believed the revolt was certain to be defeated, or if they goofed and went too far trying to catch traitors.
There have been hundreds and thousands of rebellions in history. And some of them have failed so totally and so fast that one might suspect they were actually planned by the government to identify and eliminate the disloyal.