How does the AI handle debt?

What happens when the AI factions have higher expenditure than income?

In my Roman campaign, I've chased the Greeks out of the peloponese and am currently watching them sit there with three siege machines (expensive) and an army that is too small to take me on. Bereft of Athens their economy has slipped right down on the financial ranking graph. I've deliberatley not taken on their fleet because it's costing them money.

How far can they go before their men all rebel? Will killing them all help the Greeks recover? Do I want them to anyway?

Well thanks to their scripted finance bonuses. They are probably not going to get bank rupt. I say you infultrate their settlements with spies, assasinate the most governers as possible, or just get rid of them.

So far I've only seen a single faction destroyed out of rebelling troops. The Ptolemies. That's after the Seleucids have taken over all their other provinces with the exception of Cyprus. I have no idea what sort of mismanagement the Ptolies perform on that island, but for some reason it's prone to rebel if it's the last settlement they have left.

I've never seen the KH rebel, even when they have been reduced to a single province like Rhodes. Sooner or later they will either invade or gain another settlement due to rebellion against another faction. The most common of these being Halikarnassos, Sinope, Syracusae and Cyrene.