The adoption of any charter or amendment does not destroy any property, action, right of action, claim, or demand of any nature vested in the county-city. All rights of action, claims, or demands are preserved to the county-city, and to any persons asserting any claims against the county-city as though the charter or amendment had not been adopted. The adoption of any charter or amendment affects neither the right of the county-city to collect special assessments previously levied under any law or charter for the purpose of public improvements, nor impairs the obligation of any existing contract to which the county-city is a party.