First of all, if you know in advance you will be unable to pay your taxes, you need to contact the assessor's office and work out a payment plan with them. They will allow for partial payments over time as your budget allows. This is better than not paying at all.
Here is an excerpt on payment plans from the Cook County Treasurer's website:
Q: Is there a payment plan?
A: Taxpayers are allowed to make multiple partial payments over time as their budgets allow. If you choose to pay a tax installment with multiple payments, you should be aware of the following:
(1) Checks must include your:
Property Index Number (PIN)
and, if available, e-mail address, as well as the tax year, and the tax installment on which you are making a payment (for example:12-34-567-890-1234, 2002-First Installment)
(2) If you pay in person, you must have a complete, original tax bill.
(3) Per state law, unpaid balances on an installment are assessed penalty at the rate of 1.5% per month from the due date until paid in full. If you need your current balance, you may go to Payments Status at this Web site or call our automated phone system at 312.443.5100, 24 hours a day.
(4) All tax balances on a given tax year must be paid in full prior to the annual tax sale. If taxes for a given tax year are not paid in full, the delinquent amount can be sold at a tax auction and the cost to redeem may be considerable. Taxes that are sold that are not redeemed may result in loss of property ownership.
(5) Once delinquency notices are being prepared for mailing and publication in area newspapers, by law, your next payment must include the $10 publication fee pursuant to state law and such payments must be made by certified check, cashier's check or money order prior to the start of the tax sale.
Alex, if your taxes remain unpaid for 2 installments, they will be sold, and a lien will be put on your property. And yes, you will eventually lose it if the taxes are not redeemed.
Here is another excerpt from the FAQ section of the Cook County Treasurer's website:
Q: What happens if the taxes aren't paid?
A: Under Illinois law, property tax delinquencies may be sold at tax sale. If a delinquency remains unpaid and is sold at tax sale, the tax purchaser will hold a lien on the property. Removing such a lien will add hundreds, even thousands of dollars to the amount now due. Failure to pay (or "redeem") following a sale may ultimately lead to a loss of the property.
Please read this website. It pretty much answers any question you could ever have about your taxes: