Will the underfunded pension funds in IL and KY ever be brought up to workable levels?

I doubt it.
Taxes are going to go up at least 30% or some kind of default will eventually occur.

CA and CT are also really bad on pensions and general debt but (Presently) have much richer residents, but residents can leave states.

Can a state do different?

Read about SD being almost debt free.

From 1865 to 1898 KY was run so badly that in 1898 a new constitution was written that prohibited any state debt being taken on for more than one year. Starting in 1950s this was just ignored.