Hi and welcome to Just Answer!It is possible to get OIC on trust fund liability, but that is VERY low possibility that the IRS will approve an OIC for an employer that is still in business and has ongoing payroll.In additional - if you owe taxes, penalty and interest - any payment is applied to the interest, then to penalties - and whatever left will be applied to actual tax liability. So you may not pay tax liability without paying penalties and interest.
Nevertheless - that is possible and an offer in compromise can be done on ANY tax liability, including payroll taxes. There are 3 types of OIC - (1)doubt of collectibility; (2)doubt of liability; and (3)effective tax administration. Most OIC are filed because of the doubt as to collectibility.You may want to review this IRS document Control No: SBSE-05-0108-011
The best path forward might be to ask the IRS to abate penalties, however it would be very unlikely that interest charges are abated. File a form 843 -http://www.irs.gov/pub/irs-pdf/f843.pdf to request the "accuracy related penalty" be abate based on reasonable cause. If you provide the reason like "I forgot" - I do not think it will be considered as reasonable - so be careful when prepare an abatement request. Because your father had health issues - he has a good chance to provide a reasonable cause.Here are instructions - http://www.irs.gov/pub/irs-pdf/i843.pdfIf the IRS accepts your reasons as reasonable - and agrees to abate penalties - at least part of the issue would be resolved.