It shall be a condition precedent to any agreement entered into pursuant to the provisions of sections 72-1401 to 72-1408, whether or not such condition be specified in any such agreement, that the state shall incur no liability under such agreement unless an appropriation shall have been made by the Legislature for the payment of any sums to become due and payable by the state under such agreement, in which event the state shall be liable thereunder only for the period for which an appropriation has been lawfully made, and that the continued effectiveness of such agreement shall be subject to the condition that appropriations shall be made from time to time by the Legislature for the payment of any sums to become due and payable by the state thereunder thereafter, in which event the state shall be liable thereunder only for the respective period or periods for which such an appropriation or appropriations have been lawfully made. In the event that the Legislature shall fail prior to the commencement of the term of the agreement to make an appropriation for the payment of sums which would otherwise become due and payable by the state thereunder, the effectiveness of the agreement shall thereupon immediately terminate, or in the event that the Legislature shall fail thereafter to make appropriations for the payment of sums which would otherwise become due and payable thereunder by the state, such agreement shall immediately terminate upon the last day of any period for which an appropriation has been lawfully made by the Legislature. The provisions of this section shall not prohibit the entering into of any agreement authorized by sections 72-1401 to 72-1408 prior to the making of any such appropriation, but the state shall not incur any liability thereunder thereby.