All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
After the death of his father, a mentally deranged person should be placed under the guardianship of his grandfather if his father did not make a will transferring the guardianship to another person. If the grandfather is dead or unqualified to be a guardian and did not make a will transferring the guardianship to another person, then the guardianship is the right of the governor or the person he has authorized. If no one of these people exist, then the guardianship should be entrusted with any suitable Muslim, provided that he is fair and of good conduct. In this case, if it is difficult for the governor to assign a guardian to a mentally deranged person, then the guardianship will be assigned to his mother if she is qualified and up to the responsibility. She must be in full possession of her mental faculties and judicious.
This being said, anyone who is responsible for a mentally deranged person should develop his property (and wealth). If he cannot do so, then he should assign another person, even for a wage, to undertake the task.
If the mother is responsible for the mentally deranged son, then it will be permissible for her to take the smallest amount regarding the wage of her equivalent and to suffice her needs. For example, if she can fulfill her needs with two hundred and the wage for her work is three hundred, then she may take only two hundred. This applies if she is well off. But if she is not well off, then she may take what suffices her needs, even if she surpasses the wage of her equivalent, because needy parents are entitled to financial maintenance from the property of their well-off children.
Allaah Knows best.