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.
You may use the TurboTax® Free Edition - 100% Free Tax Filing | Pay Nothing $0 - Intuit
Related information:
