Legal Question in Real Estate Law in Illinois

No, and neither can you.

No, you cannot go to jail for unpaid rent. That would be a civil matter. If it is in court, however, there come certain points in court proceedings in which your appearance is compelled and a failure to appear then leads to a warrant being issued for your arrest. Even then, the arrest is not for non-payment, but for failure to abide by the court's order to appear.