No bond or other security, oath, or other qualification is necessary to enable such corporation to accept any appointment or trust. It is lawful for any such corporation to become surety upon any bond or undertaking for or on behalf of any person, persons, or corporation, in any suit, action, or special proceeding, in any court in this state. Whenever a bond or new sureties on a bond may be required from any person, persons, or corporation, acting in any trust capacity whatever, if the value of the estate or fund is so great that the judge of the court having jurisdiction of the proceedings deems it inexpedient to require security in the full amount prescribed by law, the judge may direct that any securities for the payment of moneys belonging to the estate or fund be deposited, subject to the order of the person acting in such trust capacity, countersigned by a judge of said court, with any trust company organized and qualified to do business under the provisions of this chapter. After such deposit has been made, the judge may fix the amount of the bond with respect to the value of the remainder only of such estate or fund.