European governments will continue to back Ariane because strategically it makes sense. Russia will bankroll energyia likewise. Dominance is not static and private capital will not entirely replace state actions.
A nitpick, Energiya doesn't make rockets this days, rather Soyuzes, Progresses, satellites, upper stages (Block D)... Launchers are made mostly by Khrunichev (Proton) and Progress (Soyuz-2).
Russia tries to develop new rockets, but so far it's really slow and quite expensive. It's possible that when NASA will stop paying for Soyuz transport to ISS, it will become even slower. It's not a particularly good time in Russia for new rockets paid by the state.
All true, but do you seriously think Putin will renounce a domestic space industry? They might pick jv partnerships like ariane to stay afloat. Or sell engines or something but i dont see them giving up. To your side of this, the cash flow to a russian space sector will end when a man rated launcher from the U.S. starts making regular trips to the ISS, I guess.
> do you seriously think Putin will renounce a domestic space industry?
Probably not. It's possible to bring the space industry to the state of aviation industry, but 1) some resources are still available to maintain some level (as you mentioned) 2) to keep the same level, one needn't spend too much effort and 3) there are some interested parties in Russia which wouldn't want too deep degradation of space industry (e.g. periodically some hints to that come from Samara).
So a likely outcome could be maintenance of some expertise, at least for military purposes, and possibly attempts to cooperation with foreign partners - China, Europe etc. No total destruction; "just" - potentially - another deep crisis.
It depends if we consider state sponsored agencies maintained for national security reasons part of the ‘space industry’. There are reasonable arguments either way.
Russia tries to develop new rockets, but so far it's really slow and quite expensive. It's possible that when NASA will stop paying for Soyuz transport to ISS, it will become even slower. It's not a particularly good time in Russia for new rockets paid by the state.