Late entry into this thread, but..... Couldn't she take her utility bill to a help agency? Every place has them. They'll either make arrangements with the utility company or pay the bill outright in her behalf.
In the city where I live they've made a huge campaign out of teaching people *not* to give cash when asked. They've even printed up a poster-sized help list (that folds down to wallet-sized) with all the agencies listed along with what help that agency can give. They have listings for rent, utilities, medical, violence, substance abuse, clothing, meals, groceries, employment, training, you name it. The police, libraries, etc. have stacks of these lists and they encourage people to carry a few with them in case they are approached for help. The idea is to hand over the list, not the cash.
My suggestion is that you look in the front of your local phone book or online, anywhere there is a list of agencies for your community. Get familiar with it and make the appropriate recommendation(s) any time you are asked for cash. Try 2-1-1 (phone). Many communities use that number for a general, anonymous help line. You tell them what you are looking for and they tell you what's available in your area.
Edited to add that unless you are a doctor, the correct response, imo, to "give my head a break, please" (migraine) is "See a doctor, go to ER".