The girl has to want her life. You can shove an NG tube down her nose and give her liquid nutrition all year long and you know what? It's a band-aid. It's life-support. She isn't dying because she won't eat, she is dying because she wasn't fed.
This child has suffered and this is how she has adapted...yes, it is a maladaptive mode, but where other fall to drugs or sex or other vices, she has found that her comfort is in controlling one thing rigorously that no one else can. Now she is addicted and afraid to let go of the control.
You cannot help unless you have a way to see her to an inpatient program. An inpatient program for the general population of depressed/addicted patients won't work. They will not understand and they will tell her damaging comments which she will misinterpret, like, "You are starting to look healthier." That will terrify her, not encourage her. She is afraid of being healthy.
An eating disorder specialty clinic is the only way to treat an eating disorder. They know well and good that watching every morsel and force feeding is counter productive.
This girl has likely been a good little darling for a long while before the onset of this illness..., witnessing or suffering directly some wickedness. She has been resilient.
But make no mistake. Every time you hear "kids are resilient" you can bet that a price will be paid for that resilience. Children who have no choice but to be resilient pay the piper later.
I still cannot get on a scale. I have a bonafide phobia of scales and food, at the same time I yearn for freedom to eat without thinking about eating. I know there are those who think us selfish little brats for vanity. In reality, we toe the line just barely because we are supposed to stay alive but feel deeply that we shouldn't