If there is no surviving spouse entitled to an allowance under Sections 2.124.760 and 2.124.770 of this chapter, or if such spouse dies or remarries before every child of such deceased member attains the age of eighteen (18) years, then the allowance which the surviving spouse would have received had he or she lived and not remarried shall be paid to the member's child or children under such age, collectively, to continue until every such child dies or attains such age, provided that no child shall receive any allowance after marrying or attaining the age of eighteen (18) years. Should such member leave no surviving spouse and no children under the age of eighteen (18) years, but leave a parent or parents dependent upon the member for support, the parents so dependent shall collectively receive a monthly allowance equal to that which a surviving spouse otherwise would have received, during such dependency. (Prior code § 34.05.529)