Illinois does not tax non-resident remote workers. So you'll owe no taxes to Illinois unless you physically perform work within Illinois during the tax year..
Michigan will regard you as a resident (making all your income taxable by Michigan) unless you change your domicile to another state or country. Michigan has a form which will help you determine this:
https://www.michigan.gov/taxes/-/media/Project/Websites/taxes/Forms/All-Years/3799.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
