Anyone know what is required ... as far as paper work for a mother with full custody of her child to k-1 over her from Russia?
In this case the Father is dead, but no documents are available since he is not Russian.
Before his death, the court granted the mother custody.
Even so, will they require the father give permission?
Of course in this case the proof of Death would be required and might not be easy to locate.
Hopefully the Court removing his parental rights will be enough.

If she produces a death cert for him and the child is in her intl. passport, there should be no issues whatsoever for custody and subsequent visa issue/departure.

It would be nice if she had that certificate but she only heard through others that he died but she does not even know where he was living, I think back in his home country.

Today she picked up her new international passports, one for her and one for her daughter, so I assume the daughter is not on hers?
In any case, if she has the legal documents showing the fathers rights were terminated (when he was alive) would that be sufficiant to leave Russia?

Yes that would be sufficient. My wife had documents ready for travel to USA and for the custom officers. She was never asked to show them. Not saying you should not have them, just saying it happens...