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Lawyers always existed in Soviet period and theoretically could be hired. However the Soviet period lasted more then 70 years and the situation changed many times. For example, in 1934 penal code, the "terrorists" were deprived of their right of defense. And in general, the Soviet state was famous for systematically violating its own laws. In many political cases, the accused were sentenced not only without lawyers defending them but also without any court proceedings. But lawyers were used in non-political cases.
You are asking about the last period of existence of Soviet state, when Chernobyl disaster happened. In this period one could hire a lawyer, if you could not do this, a layer would be appointed by the court. The right for legal defense was written in the law in this period. Defending lawyers were certainly present in the process about Chernobyl disaster.
Upvote:-3
If you were considered harmful to the Communist Party in any way, the State Security (KGB) could do everything they wanted with you. Actually, one was lucky if they had a trial (with or without a lawyer), because many were arrested and sentenced (also to death) without trials. Of course, many freedoms and rights were guaranteed by the law, but it was all pure theory and had nothing to do with practice (no independent media, no independent schools, no private business and institutions, no objective trials for the accused etc.). The Communist Party controlled virtually everything while nobody controlled the Communist Party. I didn't watch the series itself, but I'm guessing the case you are asking about is the case of finding a scapegoat. Nothing in the Soviet reality could go wrong, because it was supposed to be perfect by design. So, if a catastrophe such as the Chernobyl one occurred, as much as possible was swept under the rug and for the rest a scapegoat was found. It was always human error, never the Soviet system error. I know it's really hard to imagine for someone brought up in a contemporary democratic society, but a single person really meant nothing in Soviet Russia.
Take a look here to imagine the scale of what the system was capable of: Soviet mass killings, Katyn massacre, Soviet war crimes