While it isn't directly to your question, as I was speaking to the experience in Afghanistan, I do touch briefly on the issues back in the USSR in this answer. To repeat what I said there:

Back at home, the situation faced by the troops was not at all known. The struggle was publicized back in the USSR in only the vaguest terms, speaking little of actual combat, and mostly just showing Soviet troops doing charitable work and helping build the country into a proper socialist state. The dead were brought home in secret, with zero fanfare, and buried in graves which made no mention even of their military service. The message his family would receive was even vague as well, simply noting the soldier "perished while fulfilling his international duty in Afghanistan." A soldier returning home from his service would receive little support for the PTSD he most likely would have.

But again, I was approaching more from the perspective of the military, so someone better acquainted with the political and social situation in the USSR at the time can probably expand on this considerably.