(a) For an officer, director, board appointee, member of the medical staff, or district employee, the board may:
(1) purchase and maintain liability insurance to protect the person from any liability that arises from performing a duty for the district or at a district facility; and
(2) enter into and perform an agreement to defend or indemnify the person with regard to a claim, cost, expense, or liability resulting from duties performed for the district or at a district facility.
(b) The board may establish a self-insurance program to fund an indemnity obligation.