Likely the answer would be "no." The general rule under the Illinois unemployment statutes is that, where a person causes the unemployment themselves, then they are ineligible. This means that where a person voluntarily becomes unemployed or quits a job they cannot recieve unemployment benefits.
However, the Illinois Unemployment Insurance Statute does provide an exception to this rule for employees that quit their employment "(for cause) attributable to their employing unit." Therefore, if you quit you could attempt to make the argument you were being pushed into illegal activity. However, there is no good way to predict if this argument would work. The safe bet would be to assume you would be ineligible for benefits.
NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educational purposes alone.