There are technically free bank accounts, but they often require a minimum balance, or have other gotchas. They all require identity information that may not be accessible to certain immigrants. Children also have trouble getting bank accounts.
For someone deeply in debt, a bank account is also unworkable because various legal entities can seize money from the account for the debts.
Worse still is that when I went to the bank to ask if they would limit it to the amount of money that I have rather than letting them overdraft my account, they didn't give me a clear answer, so for all I know, the debt collectors can essentially transfer the debt to the bank where I would be unable to close the account and would start accruing overdraft fees, which would then eventually get put back into collections.
Again, this hasn't happened, but the bank won't tell me whether or not this is possible, saying merely "it depends on the court order".