Reciprocal agreements generally do not affect the local taxes, so she still could be responsible for paying local taxes in KY. You would need to check with the locality that she is working in to see if they only tax residents or if they tax people who work their as well.
For KY, she will need to file a return showing the taxes paid, but when asked about editing income, the KY income will be reduced to $0. This will allow her to get a full refund of the taxes paid to KY.
She will also need to file a IL return. Since no taxes were withheld, she will need to pay the taxes and potentially, the locality that you live in.
She should also contact her employer so they can withhold for IL instead of KY.
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