Who the IRS can hold responsible
Two elements have to be present. You must be a responsible person, meaning someone with the authority to decide which bills get paid, and the failure must be willful, meaning you knew the taxes were unpaid and paid other creditors anyway. Willful in this context does not require bad intent.
The net is wider than most people expect. Owners, officers, bookkeepers, controllers, and sometimes outside advisers have all been assessed. The IRS often interviews several people and assesses more than one of them, then collects the amount once across whoever pays first.

