Has she said what she'd do if the cat became sick and needed vet care? How she'd afford the vet care, and NOT have it PTS because she can't actually afford the cat?? Is she able to understand that she needs to do what is best for the pet and not what is best for herself???

Would either place allow her to foster a cat?? I think that is a good alternative.

Can you at least let her know that if she cannot take care of a pet, and it gets sick, it will suffer, and if she really cares about the pet, she won't get one till she can afford one??? Not that you lecture her, because I think that would make someone want to do the opposite even more... that's just the way a lot of people are.

Can you really try to drive home the option to foster, with her and with the shelter?? That would benefit them both.