I would buy them a case of food, and suggest the food pantry. They're not going to eat it, and a dog somewhere isn't going to go hungry. I've been hungry (starving college student was a literal for me), but I never let my animals be hungry. I guess I feel for this person. The fact that the first option is for the food is what tugs on my heart.
The one who emailed and wanted me to buy her Ikea sewing machine without a pedal for $40 so she could buy groceries, I didn't feel so much for. Especially when I offered to bring her some groceries and she could keep the machine and never heard back from her.