(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 liability that arises from performing a duty in that capacity; and
(2) agree to defend or indemnify the person with regard to a claim, cost, expense, or liability resulting from duties performed in that capacity.
(b) The board may establish a self-insurance program to fund an indemnity obligation under Subsection (a)(2).