By late USSR, the KGB wouldn't put a bullet in the back of your head, either. They'd hand you over to "experts" who would declare you insane and shove you into a straitjacket - and even that treatment was generally reserved for active dissidents.
By the way, the police and the KGB often didn't get along. There was a famous case where a couple of cops who were very drunk robbed a high-ranking KGB official (he was carrying food from one of those "special" stores). When their senior found out, he decided that it'd be better to cover it up, and had the KGB guy killed and dumped the body in the woods. The KGB eventually unraveled the case - and many other similar ones, of cops partaking in robberies and beatings.
(https://www.tellerreport.com/news/2020-12-26-%0A---war-of-th...)
So on the whole, I suspect you'd be far more likely to be brutalized by the Soviet cops than by KGB.
Stories about KGB are popular for a reason, you know.