Is it permissible to take out a loan with interest from a bank to pay off the debts of a brother who is unable to pay, and the questioner is also unable to pay on his behalf?

It is not permissible to take out an interest-bearing loan to pay off a brother's debts, because Allah has forbidden usury and declared war on those who consume it. If the brother is in hardship, he must be given respite until ease. An interest-bearing loan is only permissible if the failure to pay the debt leads to severe harm, such as imprisonment, and the interest-bearing loan is the only way to avoid imprisonment.