is a trustee liable for the debts of a trust
No. A trustee is only liable in her capacity as a trustee and only the trust assets are exposed to its debts. Of course, that protection exists providing the trust is valid. If someone sets up a trust in order to incur debts they will not be personally responsible for paying, a creditor may be able to recover by a court action. Also, a trustee is personally liable for any mishandling of the funds of the trust.