Starvation is where your body needs to consume vital parts of itself, it's not going to happen after a week of eating a few less calories a day. Anorexia and bulimia can go on for literally years before it comes to the point where the person will be in danger and thrown into hospital to make things worse. So it's not one diet but a series of them usually, or many years of obssessive dieting that's more likely to get you to that point. And if you're not actually losing weight on any of the diets then you're not really in any danger of starvin- just getting sick from the crap you're eating in between the diets.
And ketosis isn't the only way to lose weight. It's not even the main purpose of ketosis. Ketosis is a normal bodily function which our body should do regularly because it facilitates important body maintenance that keeps us healthy. It so happens that it efficiently consumes excess body flesh and fat so it is a great way to lose weight for those of us that have been eating incorrectly. It also gets the body into healing mode as part of that maintenance so it's also the best thing to do when sick or injured.
Just eating correctly will allow your body to lose weight, but fasting is far quicker and more beneficial in so many ways.