Is it permissible for a Muslim woman with special needs, who has obtained employment, to continue receiving two salaries from the state: one an old grant and the other her new job's salary? And is her collecting of both salaries considered permissible in Islamic law?

What you asked about has two scenarios:

1. If the regulations permit the person who received the grant to work while the salary continues, then there is no objection to her benefiting from the salary, as it is a gift from the state. 2. If the regulations stipulate that the salary is not due when working elsewhere, then it is not permissible for her to take it except in cases of extreme necessity that permit the forbidden, such as being threatened with perishing.