S-Corp claimed a Business Tax Credit (Form 3800) in 2016 which passed through to personal return. Does unused portion of that credit carry forward if I dissolve S-Corp?

If you can't use part or all of your general business credit because of the tax liability limit carry the unused credit back one year. 

Per the instructions IRS for Form 3800:

"To carry back an unused credit, file an amended return (Form 1040X, Amended U.S. Individual Income Tax Return, Form 1120X, Amended U.S. Corporation Income Tax Return, or other amended return) for the prior tax year or an application for tentative refund (Form 1045, Application for Tentative Refund, or Form 1139, Corporation Application for Tentative Refund). 

Generally, if you file an application for a tentative refund, it must be filed by the end of the tax year following the tax year in which the credit arose. No part of the unused credit for any year attributable to any credit can be carried back to any tax year before the first tax year for which that credit was first allowable. 

If you have an unused credit after carrying it back 1 year, carry it forward to each of the 20 tax years after the year of the credit. Any qualified business credits (as defined in section 196(c)) that are unused after the last tax year of the 20-year carryforward period (or at the time an individual taxpayer dies or other taxpayer, such as a corporation or partnership, ceases to exist) may be taken as a deduction in the earlier of: The tax year following the last tax year of the 20-year carryforward period, or The tax year in which the individual taxpayer dies or other taxpayer ceases to exist. 

For more information, please see the instructions for IRS Form 3800 - "General Business Credit" which can be accessed at the following link:  https://www.irs.gov/pub/irs-pdf/i3800.pdf: