You missed my point. After the overseers take charge, it won't matter whether tweedle-dee or tweedle-are wins any particular seat. Voters will choice legislators, and the overseer will set policy.
And now find a law that would allow appointment of such an overseer. It's not a municipality - it's a state. It can go bankrupt, but it is still a state - it's sovereign. You may lock it out of the financial markets, but you can't strip the legislature and the governor of their constitutional powers.
Anyway, any reason to believe Illinois goes bankrupt before, say Texas? Arguably, IL is more willing to tax to pay it off - and that's, in the end, what determines whether state debts get paid. Honestly, I'd be more scared if I held TX debt these days.