I am just posting, OP, to say you are not alone. My son (early twenties) has a serious eating disorder compounded by other mental health issues and also certain neurodivergence (currently waiting for assessment). To add to the complexity, I also had a similar ED in my youth, so I have experienced a few painful reflections.
I do not have the solution, I am still trying to find ways to help and support him. However I will say this.
1: Bulimia/BED (and this sounds much more like bulimia) presents a little like an addiction. Indeed, I used to tell people that I was 'addicted' to food, and they would laugh stating that we all are. Yet, the addiction means that even if you were to lock the cupboards and fridges or keep next to nothing in the house, the individual would find something to eat e.g. eating out of dustbins, coercing or stealing money to buy food and so on.
2 The financial cost of bulimia is not mentioned often, but it is huge. My son, when he has had access to cash, can spend £100 or more on a binge. What is more, the food that he has eaten from the cupboard or fridge also has to be replaced.
3 The ED can take over, and perhaps more so if it is combined with other MH issues. In many ways the ED is a coping mechanism (a negative one) and the individual can escape into the world of just eating and vomiting, focusing on body shape, dropping with exhaustion. It takes over everything. My son is isolated and prior to the ED he was avoidant, now with the ED, he rationalises his avoidance ('How can I work, Mum, when I cannot even control what I eat?). His rationalisation is not a way of 'opting out', it is a way of hiding a terrific and fundamental anxiety about commitment, engagement, just being.
4 Whilst Anorexia Nervosa has the highest mortality rate of all mental illnesses, bulimia can also be fatal. I suspect many of the deaths from this disorder are not attributed to bulimia but rather to heart failure or suicide. My son has already damaged his heart.
5 On a more positive note, when I had this disorder (and it did not even have a name back in those days. It was 'anorexia' because I was horribly emaciated), there was little understanding and little compassion. My family could not cope with me, and it was not good for me to be at home. I ended up in various homes for people with mental health issues (after spending a lot of time in hospital). However, although the homes left a lot to be desired, eventually, I stayed in contact with my family, and, after many years, I recovered. Part of the recovery involved finding something that gave me a little self esteem.
If your daughter will not engage with anything, then this may be seen as self neglect. I initiated a carers assessment under the Care Act 2014 for myself. This made my distress known. Later, I contacted the social worker who conducted the assessment and we raised a safeguarding issue about my son. It only resulted in a couple of formal meetings, but it made agencies more aware of the situation.
Finally, I will perhaps go a little against the grain here. Bulimia arises from a dark place and it makes the individual feel terrible (ashamed, a failure, disgusted). The individual is well aware of the effect they have on others, and often (after the incident) really regrets what they have done. Try to remain open and understanding.
Yet, the reason, I would advocate for trying to work with your daughter to find help and supportive accommodation is because bulimia nervosa is hell to live with. For example, when I go out for any time, I take the ingredients for my main meal with me in a back pack, just so I know there will be something for me to eat when I get back home. Obviously, you cannot do that for the whole family. We had to get a larger dustbin from the council, due to the enormous amount of rubbish the binges created. My son has been known to take money or my card without permission, so I keep that close to me. I live in constant fear for his life and finally, bulimia keeps him stuck, he needs a team around him to help him move forward.