If an elder person living on Social Security, who has not been filing a Federal Tax form for years, receives an inheritance of $ 30 - 40,000 is there any requirement to file a Federal Tax form? To show that income?

Negative.

Inherited money is NOT subject to income taxes UNLESS it is being distributed from a 401K or traditional IRA.

Only taxes due would be estate taxes, which are paid by the estate, and then only if it exceeds the exemption minimum, which is currently in the $2 million range.