I think there are solid ways to help people but that usually means investment in them, rather than increased dependence on the system. I'd gladly chip in for this lady to get a solar panel and battery, or a waterless toilet, or microhouse, or access to cheaper fuel.
There's some pro-liberty stuff that would be great for the working poor:
* less emissions laws on vehicles - it'd be cheaper to make fuel efficient vehicles at the expense of some NOX emissions
* fewer zoning laws - it'd make micro housing more accessible
* fewer renewable energy laws / less protectionism on solar - make off-grid systems more appealing
A $10k investment in this lady's life would dramatically alter it. It would give her a toilet, better housing, and energy.
Conversely, giving her an extra $100 or so per month might just go to beer and cigs so she can deal with how crappy her life is and doesn't really give her enough to get ahead.
And that line about her brother having a quadruple bypass is icing on the cake. How much do you think we spent on that? 120k? We should keep the expenditures the same but give people a choice on how to spend it. Maybe the brother would have rolled the dice with Indian quality of care (i.e a 10k surgery) and split the savings with him - give him 50k cash for saving public money.