If you owe 941 taxes and you are the owner of a sole prop, general partner of a partnership or a single member LLC, then you are 100% liable for the unpaid 941 taxes. There is no "trust fund discount" like owners of corporations get.
However, the IRS will usually need to "turn the switch" on to personally assess this against you. These unpaid 941s can be included with your unpaid 1040s and wrapped into an Offer in Compromise or other type of resolution for your tax debt.
