No, it's only true of concentration camp victims level of starvation, where the body responds by literally giving you no energy to go about your daily life and conserves fat that way.
Not losing weight or appearing to not lose weight is often down to...
water retention after heavy exercise
water retention after more salt/msg than usual
water retention due to hormones
weighing self at a different time of day to usual
weighing self too often and the scales can't pick up small losses
accidental miscounting of calories - this is a huge one. Weigh everything, eg if you are calorie counting and use some butter or some sort of spread or whatever on your toast, weigh the jar/tub before and after use rather than guessing, and always use confirmed/reliable calorie info sources like the USDA confirmed ones on myfitnesspal
overestimating calories burned during exercise
the solution is to weigh yourself monthly to even out those daily and even weekly perfectly normal peaks and troughs
and to be meticulously accurate when calculating your TDEE, BMR and very careful to be accurate with calorie measuring/recording - and whatever you think you burned during exercise, it was probably half that despite what some apps tell you
I lost nearly 9 stone and it took an awful lot of figuring out this kind of thing and research from reliable sources
if I'd given myself a pass at any point with the 'starvation mode' myth, I'd have lost maybe 3 stone then put it all back on again as per my previous pattern