If you suppress your calories enough you can enter a "starvation mode", although there are a couple of points I'd make:
From the research, it takes a long time to see long lasting impacts from seriously reduced calories (let's say 1/2 of your maintenance needs). The mid-century Minnesota study ran for about a year. The results from that study are rather unnerving:
There were extreme reactions to the psychological effects during the
experiment including self-mutilation... Participants exhibited
a preoccupation with food... Sexual interest was drastically reduced, and ... showed signs of social withdrawal and isolation.
The participants reported a decline in concentration, comprehension
and judgment capabilities...There were
marked declines in physiological processes indicative of decreases in
each subject’s basal metabolic rate (the energy required by the body
in a state of rest), reflected in reduced body temperature,
respiration and heart rate. Some of the subjects exhibited edema in
their extremities, presumably due to decreased levels of plasma
proteins given that the body's ability to construct key proteins like
albumin is based on available energy sources.
It's important to note however that the above was a study that required participation and very few people would voluntarily endure such mental and physical pain for an entire year.
The more realistic problem to "crash dieting" is that you're really not learning and adjusting to a long term and healthy way of eating. Living in a binary world of either (a) excess or (b) extreme deficiency is hard on the mind and body.
The optimal method for fat loss is to concentrate on a more prolonged and sustainable approach. Being slightly more aggressive (before a beach vacation), or slightly less concerned (around the holiday dinners) is normal. Focus on strength training which increases your calorie consumption at rest, and keeping a watchful eye on calories, especially cheap/empty sources that sneak into your diet and end of putting you in excess.
Summarized, the biggest points I would concrete to anyone regarding body composition (ie:, how much fat vs lean muscle mass you have) is:
Be aware of your calories. Know how much you're ingesting on average. Know what you can eat more of (veggies, chicken, etc) and know what is the equivalent of caloric atomic weapon (alcohol, refined carbs, munchies, etc).
Focus on protein. You'll almost never have enough and nearly everyone is lacking in this area.
Strength train. As noted above, you'll get a ~8% caloric boost 24/7/365 just by doing effective strength training.
Don't sweat the details beyond that.