He studied theatre criticism at the State Institute of Theatrical Art, before being expelled for dissident activities in 1980. He was editor of the samizdat journal Levy Povorot from 1978 to 1982, which led to his arrest for 'anti-Soviet' activities in 1982. He was released in 1983.
In 1988, after the rise of Mikhail Gorbachev and perestroika, he resumed his studies at the GITIS, graduating in the same year, and became coordinator of the Moscow People's Front. In 1990, he was elected to the Moscow City Soviet and to the Executive of the Socialist Party (USSR).
He co-founded the Party of Labour (Russia) in October 1992. In October 1993, he was arrested for his opposition to President Boris Yeltsin during the September-October constitutional crisis, but was released the next day after international protests. Later that year, his job and the Moscow City Soviet were abolished under Yeltsin's new constitution.
From 1994 to 2002, he was a senior research fellow at the Institute for Comparative Political Studies of the Russian Academy of Sciences (ISPRAN). He was awarded his Doctorate degree for his thesis, "Collective Actions and Labour Policies in Russia in the 90s," in 1995.
In 2022 Russian authorities declared Boris to be a "foreign agent". In July 2023 he was detained on charges of ‘supporting terrorism’.