I believe the deep state files cases and procures evidence against politicians to control them. "Do as we say or we will go ahead with the prosecution."

This works in case there is no blackmail available on hand, or releasing the blackmail would cause too many ripples (the blackmailed person could have a deadman switch that at least names every other person involved, if not with evidence).

The next step is to kill them, but that's generally avoided because you have to deal with the evidence (more people involved). If the person is influential, you also lose their influence when you kill them (the replacement may not have the same level of influence etc.).