To unfuck a system like that you have to have a clean reset of sorts. It will feel unjust because past criminals will all go free, but you have to prioritize future stability. You offer amnesty for past crimes in exchange for absolute transparency and massive structure reforms moving forward.

Or, you do what the democratic party in the US has been afraid to do: Rip the bandaid off, accusations of weaponization of the DOJ be damned. The parent's hypothetical situation is precisely what is happening in the US right now where Garland failed to prosecute, and the entire democratic party was far too afraid of appearing to weaponize the justice system meanwhile the opposition has no qualms about doing so. Yes, the public will view it as entirely partisan but there's no other path forward.

But if you just do nothing at all, eventually the social contract breaks. The cost of the corruption becomes too high and the state fails, or you get a forced regime change.

You start with one party - doesn't matter which - getting in power, and then prosecuting corruption on both sides, not just on the other side.