Is there a filing requirement for a final income tax return for a deceased taxpayer, only source of income is social security and he's below minimum filing requirement?

I'm so sorry for your loss.

No, you don't have to file a final income tax return if they did not have enough income to be required to file. If you want, you may file an income tax return, reporting the date of death and the social security amount received however, you will not be able to e-file it. You will have to paper file and mail it in. 

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Related information:

• When a tax return can't be e-filed no matter what - TurboTax Support

No, a final return is not necessary, but you may wish to send a death certificate.  This would notify the IRS of a taxpayers death without having to file a return.  Source:  at IRS.gov under the title "Deceased taxpayers - protecting the deceased's identity from ID theft" it states : 

• Send the IRS a copy of the death certificate, this is used to flag the account to reflect that the person is deceased. The death certificate may be sent to the Campus where the decedent would normally file their tax return.  A copy of the death certificate may also be sent with the decedent's final tax return.