65 ILCS 5/7-1-35

If a part of a municipality is annexed to another municipality, and if proceedings were instituted before annexation to make improvements in or on streets within the annexed territory by special assessment or special taxation, the proceedings may be carried to a finality, whether the whole improvement is within the annexed territory or not. If the whole improvement is made within the annexed territory, the amount collected by the proceedings shall be paid over to the annexing municipality, to be used by that municipality for the purpose for which the proceedings were instituted. If only a part of the improvement is made within the annexed territory, the municipality from which the territory is disconnected may proceed with the improvement as though no annexation had taken place.