Here are my thoughts.
First, your empire, instead of having corruption for each city, it should have a nationwide corruption system based partly on you're treasury (whether it's growing or shrinking), the size of your empire, the government you're in, the difficulty level, and possibly a few other factors.
So, when your capital is captured, it takes into account a number of factors:
1-The overall corruption of your empire (the most important thing)
2-The population of your capital city and empire (higher is worse)
3-The cultural level and/or world ranking compared to everyone else (lower is worse)
4-Your military strength
5-Your government (undecided on what should be worse or better)
Here are some of things that could happen (from best to worst). A seed number will be rolled to see whether your leader will be rescued or not.
1-There is a chance that your leader will be rescued from his palace by collaborators, based on the factors above and then a final, random seed number to determine the ultimate outcome. In this case, you get to choose what city will be your new capital. Note that this may happen even if your civilization is in revolt, but it will also increase the likelihood that your empire will return to order. This option is not possible in a worst-case scenario (at bottom).
2-Your civilization experiences an increase in corruption but no disorder.
3-Units may be disbanded and may have decreased morale temperorarily, corruption will increase sharply, and cities may be thrown into a temporary revolt.
4-Cities may fall into civil disorder, more units will be disbanded, corruption will be rampant. Militant groups may constantly switch around your capital, although your government type will remain the same.
5-1 or 2 turns of Anarchy followed by a random generation of a new government after rebellious groups take control. Uncontrollabel corruption and excessive disbanding and morale decreases of units. Your palace is destroyed and you have no capital. Not possible on lowest levels, no matter how bad your corruption is.