Any area excluded from a district shall be subject to assessment and be otherwise chargeable for the payment and discharge of all of the obligations outstanding at the time of the filing of the petition for the exclusion of the area as fully as though the area had not been excluded. All provisions which could be used to compel the payment by an excluded area of its portion of the outstanding obligations had the exclusion not occurred may be used to compel the payment on the part of the area of the portion of the outstanding obligations of the district for which it is liable.