Can banks take money out of a basic account to offset debts?

Generally the answer is yes. In your account agreement there may be a clause governing what is called the "right of offset" where the bank retains the right to take funds from your account to pay debts owed to that same bank. They are also responsible for freezing or removing funds if ordered to do so by a court or a government levy. This may not apply to real estate debt in some states, and does not apply if the debt is not held by the bank and no legal order to remove or freeze the money has been made.