Konstantin over at "Inside Russia" has said the only way they ever knew a leader had been removed or had died was that alll the TV channels and radio stations would start playing "Swan Lake" and that would go on for three days. At the end of three days, the new leader was announced along with a funeral date for the old one if he'd kicked the bucket.
Personally, I think about the only way we'd notice something going on is if some of Putin's most trusted people suddenly disappear, appointed to nothing jobs in the background to keep them out of the way so that one of his hand picked loyalists will succeed him---you know, the way Shoigu was kind of shoved into the background while an absolute nobody of a numbers cruncher was appointed Minister of Defense. Even that is a long shot, Putin has been known to teach people he doesn't quite want to get rid of a lesson.
No, I think they'll return to the 3 days of Swan Lake after which the FSB will announce who they've picked to be the next raging asshole strongman to screw the Russian people while he and his buddies get rich. Likely the troops in Ukraine will be told to dig in where they are but not to try to advance. It will take Ukraine some years to dislodge them. The Russian people will believe and do what they're told.