I don't know how the partnership can be "closed with 0 income and 0 expense."  Even if the partners had resolved to close/dissolve the partnership in its initial year, Form 1065 still should have been filed for the initial/final year - and the late filing penalty would still have been applicable for the year.

That said, check if the IRS First-Time Penalty Abatement administrative waiver is still in force.

https://www.irs.gov/payments/penalty-relief-due-to-first-time-abate-or-other-administrative-waiver

The related provisions used to be prescribed in IRM 20.1.1.3.3. and IRM 20.1.1.3.3.6. 

I haven't handled a similar issue lately and my info may not be up-to-date.  

California R&TC Section 19132.5 also allows for a First-Time Penalty Abatement, in case it's a CA partnership.

Hope this helps.