Why is the lineage of an illegitimate child not established to his parents, even with their acknowledgement and care for him? And does the state take responsibility for such individuals?

There is no dispute among scholars that a child is attributed to the owner of the marital bed, unless he disavows the child through li'an, based on the Prophet's (peace and blessings be upon him) saying: "The child is for the bed, and for the fornicator is the stone." However, if the mother is not a lawful marital bed for anyone, scholars differ. Some, such as Al-Hasan Al-Basri, Urwah ibn Al-Zubayr, Sulaiman ibn Yasar, and Ibn Taymiyyah, are of the view that a child born of zina (fornication/adultery) is attributed to the fornicator if he claims him, citing that Umar ibn Al-Khattab used to attribute children born in the pre-Islamic era (Jahiliyyah) to whoever claimed them. In contrast, the majority of scholars hold that a child born of zina is not attributed to his fornicator father, even if he claims him. Therefore, a child born of zina is not legally attributed to his fornicator father. As for the state's responsibility to care for these children, it is subject to the regulations of each state. The fundamental principle is that the state is not obliged to do so unless the child has no guardian, in which case the state becomes responsible for his care as part of the Muslim ruler's responsibility.