The recipient of a gift has no responsibility to report the gift (assuming it is a real gift and not someone "giving" you money as a tax cheat to avoid reporting a wage). The giver has no reporting requirements up to $13,000 per person per year before it starts counting against the lifetime gift/inheritance limits.
However, if the woman is receiving ANY form of assistance from the government,(as I suspect she must if she is in such financial need) then she must report any and all gifts as income. Even gifts of clothing, presents at holiays, etc. Many don't...but the requirements for this are there, just not always enforced. In this woman's case, they should investigate and if she has any government assistance, she is in violation...should be fined, and the IRS should go to work on her.