Does a father remain the guardian (wali) of his daughter in her life affairs that require his permission, such as her going out and working, or does her eldest brother become her guardian, especially with the father's negligence in providing financial support, care, and discipline?

Firstly: The guardianship of marriage (wilayat an-nikah (definition)) belongs to the closest male agnate relative of the woman (her son, her father, her grandfather, her brother), in that order. The father's guardianship does not transfer to anyone else, even if he does not provide for his daughter.

Secondly: The father's guardianship over his daughter, in matters other than marriage (guardianship over her person), ends upon her reaching puberty or her marriage, according to the scholars. This means that she is permitted to live alone, but she is still obligated to obey her father in matters that are not sinful.

In summary, a woman remains in her father's house until her marriage, according to the Maliki and Hanbali schools, or until she becomes an elderly woman of sound judgment, according to the Hanafi school. She should not leave except with his permission. If the father delegates the matter to her brother, then she may seek permission from him, and she must obey her father in permissible matters.