I have to say no due to fact you stated she is having trouble making ends meet for herself. The added cost of a pet it would appear put her in a big bind. When your having trouble taking care of yourself, a pet is not for someone in that circumstance.
It would be hard for her to be a responsible pet owner. Where's the money going to come for yearly shots, litter, food, emergancies?????
I would hate to see an aniamal in that type of situation where his/her well being is very questionable. It's not fair to the aniamal.