That's what J. Edgar Hoover did to his best agent, Melvin Purvis, for getting too famous (he took down many bold gunsels, including Dillinger). Hoover wanted all the publicity to go back to the agency (him) and all his employees to be anonymous and faceless. The newspapers wanted a hero, and they destroyed Purvis when they lionized him.
Hoover fired Purvis, then persecuted him for years, bugging him and having agents call him up anonymously and giving him menacing messages. Purvis eventually committed suicide, which was what Hoover was apparently after. "The coward's way out" -- blackening Purvis for all time.
I was under surveillance for the exact same thing. I had a run in with a cop that spouted his mouth off about being involved with a dope running operation involving corrupt cops and the CIA.
I thought the cop was a nut. He wasn't.