Learn English – Equivalent for the Russian idiom “to write into the drawer”

The expression about which the OP inquires is the now largely historical term that is usually translated into English from the Russian писать в стол or писать в ящик ( http://phraseology_ru_en.academic.ru/27881/писать_в_стол ) as to write for the drawer, the significance of which is well described in an Economist article dating from 11 November 1969. One of the principal themes of the article is the central importance for writers in the USSR of enjoying the goodwill of the Writers' Union:

Prominent writers are a privileged section of Soviet society. Men like Boris Pasternak can survive a period of disgrace by living on their savings. Young men can take a job outside literature and go on writing in their spare time. Those who refuse to conform can write for the “drawer”—for posterity—or, in the case of the younger rebels, for underground publication. They can all show their work to their friends.

Along similar lines, this 2002 article from the Los Angeles Times describes the tragic life of the Hungarian writer Sandor Marai, from which I quote:

Marai survived the Nazis and their World War II collaborators, and even published some works during those years. The Communists who solidified power in 1948, though, proved to be more difficult. Writers were expected to publish works of socialist realism, ennobling both the worker and the revolutionary while denouncing the bourgeois values that framed Marai's life and his art.

Marai sought to remain silent, "to write for the drawer." But the Communists, he wrote, "would not let me be silent freely."