I don’t think we Americans really have any clue about Russian politics, Russian law, or Putin. If we believe the oligarchs are really in-charge, then they put Putin in power. If Putin rose to the position through his own initiatives, then those who are oligarchs will continue to support him, or else.
That's why I said mexican standoff.
While I know nothing of the internal politics of Russia just studying strong man governments through history it isn't uncommon for the strong man to be beholden to other power brokers within and when things go south it often becomes a circular firing squad, sometimes literally.
The fact that a few have been allowed to become oligarchs in Russia indicates this may be the case.
History is rife with examples of strongmen who once seemed untouchable who fall dramatically.