The severance pay came from IL so my thought process is the income is IL based. Severance pay may be based on length of service and/ or salary. If the money was due to work in IL, it should have IL tax withheld and it is taxable. Not knowing where all you worked and your specific details, here are the rulings for you to verify your situation and the taxability.
Looking at page 3 of the IL instructions for who needs to file, it states:
► a nonresident, you must file Form IL-1040 and Schedule NR if you earned enough taxable income from Illinois sources to have a tax liability (i.e., your Illinois base income from Schedule NR, Step 5, Line 46, is greater than your Illinois exemption allowance on Schedule NR, Step 5, Line 50), or you want a refund of any Illinois Income Tax withheld in error. You must attach a letter of explanation from your employer.
This ruling explains when tax must be withheld and taxable income.
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