Well I think there's a misunderstanding. If you can keep eating a tiny amount and no more, you will lose weight (and hair and energy and muscle mass and the ability to function) but our bodies are designed to fight really hard against allowing that to happen.
So as your body realises it's in a calorie deficit - especially if you have a long history of yoyo dieting - it does its best to conserve energy as much as it can. Your metabolism does slow, and a lot of dieting over your lifetime does make it slower overall than someone who has never dieted. Bodies are really clever at adapting. It will become more efficient, it will make you more tired and find little ways to keep you sedentary as much as it can. You will, eating too little to sustain yourself, be very tired and very hungry and your body will ramp that up to motivate you to eat. Bodies really do not want to lose weight and they really want to regain it once lost as an incredibly powerful and primal survival mechanism that it's almost impossible to resist.
So yes, your body learns to survive off fewer calories while storing as much energy as it can and that means long-term dieters have to drive down their calorie intake to unsustainable levels to keep losing. They also regain much, much faster the more often they diet.
Even on the injections, people experience stalls and plateaus. Anyone who has ever embarked on weight loss is familiar with this. It's your body adapting and fighting the weight loss. It's very easy to see this on the jabs because you aren't giving in to hunger like you might on a normal diet - the hunger isn't there so it's not like you 'cheat' or give in. But still, the loss will slow and stop on that small intake and t will take a frustrating time to start up again.
If our bodies worked in a simple, predictable way where calories in and out worked perfectly all the time, no one would experience stalls - even gains! - on the jabs but anyone taking them knows this happens. It is anecdotally true that upping your calories for a few days can sometimes restart the loss. I don't know about calling it 'starvation mode' because true starvation will waste someone away until they die. But it is some kind of survival mode, where the body fights really hard against the calorie restriction. Of course, you break through it if you can keep going - the jabs help people to keep going, it's part of their function. But calorie restriction does trigger resistance to weight loss and cause those stops and starts to take place.