You're right about unaliving their financial identity.
Need an SSN to open a bank account or establish credit. It's not supposed to have been that way, but it's how it ended up.
I imagine their bank accounts will end up being forefeited but they'll still be on the hook for debts.
And the definition of "credit" is pretty loose. Not just cards and car loans...but EPPs on cell phones, college (including parent) loans, hell even some internet plans, rental agreements, car/home/rental insurance (and car insurance being legally required to drive in most states, especially blue states....I imagine driving an uninsured vehicle will be a deportable offense, too).
Oh and to get a job. At least one with the acceptable level of worker exploitation. They'll still be able to get jobs with unacceptable levels of worker exploitation (under the table).