Is it permissible for an Islamic bank to support its provision for doubtful debts from revenues that are non-Sharia-compliant, such as interest income, and then distribute it to shareholders?

If the bank donates haram money for its own benefit, it is not permissible according to Sharia, because the channels for illicit money are the general public interests of Muslims, such as orphanages, hospitals, roads, and the like, as well as spending it on the poor and needy. As for spending it for the benefit of its possessor, it is not permissible unless he is poor and in need.