My wife fell for a fake email and ended up entering her social, dob, address... on a fake website.
How to dig out of the hole now?
Can they clean out the bank accounts?
Depending on the skill level of the hackers, yes they can clean out your bank accounts. Alert your bank of the situation and hopefully they can monitor your accounts more closely.
There is nothing much you can do since your wife’s SSN and DOB are permanent other than freeze your credit but that won't stop all fraud. You're going to have to monitor your accounts with a third eye and give your wife a time out to learn from this.