I don’t think whether it was earned on her part is the point. The point is that it hits the poor worse than the rich, who are more often farsighted enough to plan against it. If the mother is getting welfare she has already been set apart as in need of special consideration by the government, rightly or wrongly. To then turn around and steal her largesse back is ineffeicient, if nothing else.
The point remains that, a better example should have been chosen for illustration purposes. The welfare recipient will not suffer the consequences of a cheapened dollar, because, whatever she/he receives, will be enough to cover the inflation of “her” money. Inflation hits harder on those who don’t get payments that account for that inflation. My money in the bank is not going to be adjusted for inflation when I do decide to withdraw it, or use it for payments.