Allowing a child to die

I know this will make some people mad, but it's a difficult situation no matter what.  One of my clients has a child with an extremely rare condition that basically takes all quality of life away for her. She can't talk, needs to be in a wheelchair and will continuously decline. On top of this, there is a heart defect.  This mom asked me if she doesn't get the surgery for the heart defect (she can't afford it), and her child dies, would she be subject to any laws regarding neglect.  I'm not an expert on ethical laws regarding this so I'm wondering how it works if someone can't afford to pay for a life-saving surgery or chooses not to based on quality of life.