Is it permissible for my brother to declare bankruptcy to avoid paying the credit card debts he has accumulated in America?

A Muslim should be a good example for others, characterized by the ethics and manners of Islam, such as truthfulness, trustworthiness, and loyalty. He should not be a bad example through lying and betrayal, which would turn people away from the religion of Allah. Your brother must repay the debts incurred on the card whenever he becomes able, and his liability is not discharged merely by his bankruptcy unless the creditors absolve him. His attempt to waive people's rights is an injustice. If these debts include usurious interest, he is obligated to repay only the principal amount without the interest, unless he is compelled to pay it.