In the power struggles that followed the death of Soviet leader Joseph Stalin, Bobkov survived Beria's removal and execution, and later outlasted eleven subsequent chairmen of the Ministry of State Security (MGB) and KGB.

However, Bobkov denied these allegations, saying that he did not support the creation of a "Zubatov-style pseudo-party under KGB control, which directs interests and sentiments of certain social groups".

Former Politburo deputy and reformist leader Alexander Yakovlev, however, has claimed that Bobkov did not solve these conflicts, but rather created them in an effort to maintain the power of the KGB by showing its necessity.

The project was funded by KGB and Party money, "which made up almost 80% of the amount invested in the new banks, stock exchanges, and businesses in 1990-1991", according to the testimony of Richard Palmer to the United States Congress regarding Soviet infiltration of the Western financial system.

Bobkov officially retired in 1991 and organized a private security service in the Media Most company called SB MOST Group (Russian: СБ „Группы МОСТ“), which included thousands of his former KGB colleagues.