Respectfully, Isha, that capitalized “WILL” seems more like a statement of faith than of fact.
If, hypothetically, the other empires, and particularly the Republic and Federation, drove the Empire to collapse, they’re very unlikely to escape unscathed themselves. The people best-placed to take advantage probably wouldn’t be the empires, but the “pirate” factions, the most hopeful option among which would be the Angel Cartel. But actually the most likely would be the Blood Raiders or Sansha’s Nation.
Sansha’s Nation would move in its usual way, just (assuming they have the resources, and they do seem to) on a larger scale-- an Empire-sized Incursion with little organized resistance and massive “uplifting” operations. Maybe they’d take the population and disappear to process them, but actually it seems more like they’d just move right on in and make themselves comfortable.
The Blood Raiders would have an even easier time; Amarrian culture is highly focused on the distribution and control of power, on who gets it, how much, and why. That focus is an opening for the Sabik, whose answer to those questions boils down to “anyone who can take it and as much as they can grab, because that’s all that matters.” A mass crisis of faith such as the Empire’s fall would leave them with basically a whole empire of recruits and victims.
Neither one would stop there, either. The Empire’s a seriously vast pool of resources, and an entity that moved swiftly and successfully to harness them would be able to draw on enormous power. Sansha Kuvakei shows no signs of wanting to live in peace, but the Raiders would base their conquest largely on a promise of restored glory. Bloody Omir would declare vindication and some grand crusade of conquest, glory, and vengeance. They’d gather all the power they could, slap some red paint on whatever survived of the Golden Fleet, and they’d come for the rest of you with their usual nihilistic zeal. They’d probably throw the whole society into it.
They’re horrible, Isha. If you want to talk “barbarians,” well-- it’s hard to find purer examples, and hard to describe what the Sabik create as a civilization. And it’s inherently, internally unstable because it creates no basis for loyalty besides fear. Every servant is encouraged (even expected) to plot against their masters and each other. It’s a slow-boiling civil cold war of all against all until it goes hot and the civilization evaporates in a puff of horrors.
But in the meantime, if the Takmahl are any example, it’ll do pretty well for itself. Omir might accomplish some very scary things before his empire finishes rotting from within, and I wouldn’t wish the Sabik on anyone.
Anyway, the victors in an Imperial collapse wouldn’t be your people. The victors would be the vultures who came to feast on the Empire’s corpse.