When the insurer of a health care provider or inactive health care provider covered by the fund has agreed to settle its liability on a claim against its insured or when the self-insurer has agreed to settle liability on a claim and the claimant's demand is in an amount in excess of such settlement, or where a claim is against an inactive health care provider covered by the fund who does not have liability insurance in effect which is applicable to the claim, or where it would otherwise be in the best interest of the fund, the claimant and the board of governors may negotiate on an amount to be paid from the fund. The board of governors may employ independent counsel to represent the interest of the fund in any such negotiations. In the event the claimant and the board of governors agree upon an amount the following procedure shall be followed:
K.S.A. 40-3410