Why do you think it should be zero? The State of Illinois already knows that you are a nonresident (or else you would not be using Schedule NR). And the instructions literally say, "Line 24: Health savings account deduction Enter the amount of health savings account deduction you claimed this year as shown in Column A."
The net result is that whether or not you live in the state, you should remove any HSA contributions from state income by following the instructions for Schedule NR.
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