Several years ago, I had written a couple bad checks before I realized that I didn't have enough money in my account to cover them. I thought the bank would NSF them, but they paid the checks and left me in a negative balance. They charged a $35 overdraft fee for each of the checks and that was it.
After a couple weeks in the negative, they sent me a letter saying that "due to FDIC regulations, we will be forced to close the account if you do not cover these funds," and they gave me 10 days to put money in my account to at least have a zero-balance.
Sure enough, after 10 days they closed my account. Fortunately, they let me sign a payment plan and they gave me 6 months to payoff the amount.
Since the FDIC regulates these banks, they have to follow certain proceedures in order to be insured. One of those procedures is to close an account that may be deemed as a bad asset. After all, if a bank has a number of negative deposit accounts then it really does screw up their books and doesn't reflect the banks true financial position. I would think having a $3000 negative balance, made up of all NSF fees, constitutes a bad asset and your bank would be forced to close the account per FDIC rules.
Like chizhy said, go to the FDIC and fie a complaint. I think they may be interested to know about it.