No, you may not subtract your out-of-state income. However, if you are filing as a resident, you may be allowed to take a credit against Illinois Income Tax for income tax you paid to another state. See the instructions for Form IL-1040, Line 16, and Schedule CR, Credit for Tax Paid to Other States.
If you are filing as a part-year resident, you must file Schedule NR. You may also be allowed to file Schedule CR if the income you earned as an Illinois resident is also being taxed by another state. If you are filing as a nonresident, you must file Schedule NR.
Note: Unemployment income is always taxable to your State of Residency.