If, on such settlement, a balance is ascertained to be due from the estate of such decedent to the deceased or outgoing executor or administrator, the probate court may, if six months have elapsed from the grant of original letters, render a decree in favor of the outgoing executor or administrator or, if dead, of his personal representative, against the remaining or succeeding executor or administrator for such balance; and if the estate is solvent, payment thereof may be enforced by execution against him, to be levied on any effects of such estate in his hands unadministered; but if the estate is insolvent, such decree is to be paid as other claims against insolvent estates; and if such balance or any part thereof is for expenses of administration necessarily incurred, such balance, or such part thereof as may be for such expenses, shall be a preferred claim against such estate and shall be paid as other preferred claims are paid.