First, each chicken is an individual. You do not get guarantees regarding living animals. We can tell you what we typically see or what we would expect to happen but we cannot guarantee it will happen with your individual hen.
Before a pullet or hen starts laying she builds up excess fat, especially in her pelvic region. This fat is mostly what she lives off of while she is broody. That way she can stay on the nest taking care of the eggs instead of needing to be off looking for food and water. They will usually eat and drink (and poop) while off of the nest but they do not need to eat or drink much. Since they are using up fat stored for that purpose they will lose weight. When they use up that fat they usually break from being broody. Mother nature set it up that way so they would not go extinct if her eggs don't hatch. Is it possible one will starve herself to death? They are living animals so anything is possible, but that is extremely unlikely.
Someone mentioned a loss of condition. Before they start laying again they need to replace that used fat so the more fat they use the longer it will be before she starts laying again after breaking form being broody. You can consider that a loss of condition, but that has to do with egg laying, not health.
A broody can be disruptive in the henhouse. Most of mine are not but they can be. You can put up with it if you want, it is highly likely she will break when her excess fat runs out. Or if you want peace now, I suggest breaking her. I use an elevated wire-bottomed cage so air can get under her and cool her. Give her food and water but nothing like a nest. Leave her in for 72 hours and let her go. If she goes back in her old nest put her back in for a couple more days. Most of mine break in 72 hours but I once had one that had to go through it 3 times before breaking. Each one is an individual.
Good luck!
