(a) Such part of the indebtedness, principal or interest, of the original district growing out of the cost of the local improvement as has been allocated, or may be allocable, to the lands of the subsidiary district, or may, from time to time, be so allocable to and chargeable against the lands of the subsidiary district in the way of special improvement taxes, may be assumed and paid by the taxing district from a fund produced by the sale of its bonds or certificates of indebtedness.
(b) In the assumption of the debts of the subsidiary district, the taxing district shall be subrogated with respect to liens, pledges, and such other provisions relating to securities for the debt assumed as belonged to the original district of which the subsidiary district was a part.