Any of such asylums may, at discretion, receive any child placed in its care and keeping by such child’s parents or guardian, or those having the child in charge, and may keep and care for the child until the child is eighteen (18) years of age, unless sooner taken away by the request of such child’s parent or parents, or those having guardianship or control of the child. The asylum shall not receive any child under this section until its parent or parents, or guardian, or person having the child in charge, shall agree with the officers of the asylum to supply sufficient funds, or such portion of the funds as the board of managers may agree upon, for the maintenance of the child in the asylum during such child’s stay, and shall further agree to abide by all rules, bylaws, and requirements of the asylum. Should a child be admitted having a guardian lawfully appointed and qualified, who has money or property of such child under such guardian’s control, such guardian shall be required to pay to the asylum such portion of the child’s funds as the guardian may lawfully use, or the guardian may be authorized to use, for the child’s support.