Even though he was a comedian, Frunzik's personal life was very sad. His first wife, Donara Mkrtchyan, became mentally ill and was sent to a mental institution for the rest of her life and Frunzik became a single parent of two young kids.
His son inherited his mother’s mental illness and, according to people close to Frunzik, he suffered from severe depression in the last few years of his life, and became a heavy alcoholic. In 1993, his brother found him lying dead in his home in Yerevan. Thousands of people attended his funeral.