You initially didn't give a lot of info, so I had to suggest a few things. An example of a 'responsible party assessment' would be the company controller, who made the fed tax deposits but didn't make some, could be liable as a responsible party.
Chapter 7 will discharge taxes more than three years old, and you are correct about the employment taxes, but only the trust fund portion (withheld from employee paychecks) would survive the filing
Now I see what the problem is. The good thing is IRS will probably not assess for taxes after your Chapter 7. It's not likely they will get anything. And, they must, by statute, make their claim for taxes due before the petition date, so the bankruptcy
court has a chance to rule on their collectibility.
Don't forget to claim the periods of this phantom assessment on your petition, and you should be fine.
I'm not an attorney, but I do a lot of bankruptcy-related tax settlement, so I know the drill.
Thanks from Just Answer, and don't forget an Accept.