The lieutenant governor
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The state of Illinois has a executive branch. This branch became Governor if the present Governor is unable to finish.
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Their specific duties may vary depending on the state and how the state's constitution is written, Their main responsibility is to step up to the governor's position should the elected governor become incapacitated or die while in office.
The Lieutenant Governor.
If the governor is unable to act, the lieutenant governor typically assumes the duties of the governor. If the lieutenant governor is also unable to act, a specific line of succession outlined in the state's constitution or laws would come into play to designate the next official to take over.
lieutenant governor
The Lt. Gov. presides over the Senate, and takes the place of the Gov. if Gov. is unable to serve.
balls!
If the governor is unable to fulfill his/her duties (e.g. under arrest) the lieutenant governor will take his/her place until the governor returns, if s/he returns.
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Typically - upon the death or impeachment of the Governor - or - if the Governor becomes incapacitated and unable to carry out the duties of office (usually set as a period of time by the state constitution).