When Polticians relinquished their roles during the Soviet State of Emergency, some of these men became Special Advisors. Usually, it was Politicans apart of the Emergency Committee that took on this role in order to maintain membership. This allowed them to keep positions in the Government, as well as their elgibility for smaller, more reclusive roles.
In the Constitution, Special Advisors are only allowed during State of Emergencies as Per Article 159 Section 2.3
"When Members of the Emergency Committee wish to step down from Active Poltiics, they are required to become Special Advisors, Until the Committee is disbanded."