The State Department of Developmental Services may enter into a special agreement, secured by a properly executed bond, with the relatives, guardian, conservator, or friend of any patient for the patient’s care, support, maintenance, or other expenses at the institution. The agreement and bond shall be to the people of the State of California and action to enforce the same may be brought by the department. All charges due under this section, including the monthly rate for the patient’s care and treatment, as established by or pursuant to law, shall be collected monthly. No patient, however, shall be permitted to occupy more than one room in any state institution.