It was very unpopular, lead to people fleeing the country, and was pushed out of the public eye as soon as they figured out how to forcefully volunteer people instead.
It wasn't hard to dodge; you could just refuse to take the papers pretending it's not you or get sick the very day or something like that. The system had a number and once it was reached (very quickly) no further action was necessary. The only change so far us that the employers started to follow their military tracking procedure to the letter; before that it was required but not really enforced, but now all the paperwork gets done by the book.
Some people indeed left the country but those are the kind you don't want to have your back anyway.
Forceful volunteering is pure imagination. At most it's intensive persuasion or a new way to get out of jail, but if you don't want to go, nobody will force you.
Around the Moscow elite, no. In the outer provinces, we have ample evidence of forced conscription.