How can children safeguard their father's lawful money if he is partially unconscious and unaware of the value of things, given their desire not to act without his permission or disturb him by disobeying him?

The jurists have stipulated the permissibility of placing an interdiction on an adult whose mind has changed, because he is unable to manage his wealth properly. Abdur-Razzaq narrated from Ibn Abbas his saying: "If his mind is gone or he denies his mind, an interdiction is placed on him."

Therefore, if your father is in such a state, you must treat him kindly and dutifully, and prevent him from disposing of his money with gentleness and wisdom. You should also promptly refer the matter to the Sharia courts to rule on his condition. If the court rules to place an interdiction on him, there is no undutifulness in that, provided you continue to treat him gently and kindly.