Often very poorly.
Refeeding syndrome is a real issue when you go from eating almost nothing to eating a whole lot at once. If you're ever in for major surgery, it's the reason they slowly work you up to solid foods over time, rather than just letting you eat normally.
While I can't speak for every camp, I know Bergen-Belsen is referenced as having had a significant number of rescued holocaust survivors who died when their rescuers handed over food. Eating large quantities of rich food is simply too much for a starved body. Rich soldier rations, chocolate and the like often made things worse, not better. While they wouldn't die instantly, often they'd vomit up what they'd eaten, and considering they were often dehydrated as well as starved, it could fairly easily kill them. There were plenty of other complications coming from rich food, but they very depending on what an individual was eating.
I have a lot of first hand accounts, but I don't have access to any solid studies on how things went after the initial panic. Simply put, people had better things to do, and weeks after the fact it's difficult, if not impossible, to determine exactly what killed someone.
The German book "Der Ort des Terrors" talks briefly about this. While exact numbers aren't available for most camps, Mauthausen is mentioned as having 'thousands' dying upon being rescued, although from various causes. Certainly not all of them were from overeating and refeeding syndrome, but at least some of them seem to be.
Are you asking about the biology of recovering from severe malnutrition, or are you asking about the steps Allied troops and others took to rehabilitate survivors?
This is probably related: I have read anecdotes about the freeing of concentration camps where survivors said it was better to be freed by the Russians than by the Americans because the Americans would also feed you. Eating the food the Americans offered could be fatal due to the shock of suddenly coming into contact with so much nutrients after a period of starvation.
Any truth to this?
Just to add a question here. I've heard about some programs quakers or pacifists engaged in, namely volunteering for starvation so the allies could learn how to better give food to camp survivors. Is this true?
Follow-up question: I recall listening to a programme on BBC Radio 4 about Jack Drummond, the British nutritionist who was responsible for determining government rationing policy in the UK during WW2. As far as I recall, the programme claimed that Drummond invented a food for feeding victims of severe malnutrition that saved lives in concentration camps liberated by the British. Does anyone know about this, or can anyone find sources? The only source I can find at the moment (I'm posing from my phone on a bus) is this pdf, which states:
Not only Britons benefitted from his practical application of the scientific principles of nutrition: at the end of the war, he made “an easily digested porridge for the emergency treatment of the seriously starved. Known as ‘Drummond mixture’, it was deployed at Bergen-Belsen and other Nazi death camps as they were liberated, and undoubtedly saved thousands of lives.
Refeeding has already been addressed in this thread, but I'm interested in the long term rehabilitation, or lack there of, and how well concentration camp victims recovered physically and mentally.