S.D. Codified Laws § 34-31A-35
The boundaries of any rural fire protection district organized under the provisions of this chapter may be changed in the manner prescribed by §§ 34-31A-5 to 34-31A-9, inclusive, but the changes of boundaries of any such district may not impair or affect its organization or its right in or to property; nor may it impair, affect or discharge any contract, obligation, lien, or charge for or upon which it might be liable had such change of boundaries not been made. Any portion or area of land which was part of a rural fire district, organized under §§ 34-31A-5 to 34-31A-9, inclusive, and which is annexed into a bordering municipality, is liable for any indebtedness incurred while within the boundaries of the fire district. Nothing in this section precludes a municipality, by ordinance, when annexing land within a rural fire protection district, of assuming a portion or all of the indebtedness on the annexed land that is a result of being in the rural fire protection district.
SDCL 34-31A-35