65 ILCS 55/16
If from any cause any city, village or town shall fail to collect the whole or any portion of any special assessment or special tax which may be levied, which shall not be canceled or set aside by the order of any court, the city council or board of trustees may, at any time within five years after the confirmation of the original assessment, direct a new assessment to be made upon the delinquent property for the amount of such deficiency and interest thereon from the date of such original assessment, which assessment shall be made, as nearly as may be, in the same manner as is herein prescribed for the first assessment. In all cases where partial payments shall have been made on such former assessments, they shall be credited or allowed on the new assessment to the property for which they were made, so that the assessment shall be equal and impartial in its results. If such new assessment prove insufficient, either in whole or in part, the city council or board of trustees may, at any time within said period of five years, order a third to be levied, and so on in the same manner and for the same purpose; and it shall constitute no legal objection to such assessment that the property may have changed hands, or been encumbered subsequent to the date of the original assessment.
65 ILCS 55/16