If you ate your calories of all one thing for quite some time (like all fruit, all veggies, all protein, etc.) it isn't really a matter of your body going into "starvation mode", as you said-meaning that your body would start slowing down its metabolism-but more like you would be doing a different sort of damage to your body.
If you eat nothing but salad or veggies for a week...then what happens is that your body doesn't recieve enough fat-which can affect the hair, nails, and skin visibly-brittle hair, dry skin, etc. and over time, it can cause damage. Your body has to have a certain amount of fat for your organs.
If you ate nothing but fruit or veggies for a week-another concern is that you would not get any protein. Protein is what feeds your muscles. If you don't eat any protein, then your muscles starve. If you exercise to gain muscle, and then starve it...it doesn't make any sense. You will lose muscle, rather than gain it, by starving it.
If you eat nothing but meat for a week or longer-you will miss out on fiber, which will cause problems for you digestively, and then you miss out on all of the vitamins and fiber, and antiaging properties, and antioxidants in fruits and veggies.
So...it isn't a good idea to just eat a certain group of food and nothing else.
So-this comes around to answer your question.
If you are eating a balanced diet, then it shouldn't be that hard to "eat all day" (as your question posed) and get your calories in. It's hard to eat all day, and consume fat and protein in the process, and only end up with 800 calories, for instance. If you are not getting your calories in, and are ending up way too low-then your diet is lacking somewhere. To eat all day and not get them in-most likely you would be skipping out in the fat or protein department.
Also, it takes longer than a week for starvation mode to kick in. It is a phrase commonly thrown around. An illness for a few days where your food intake is light won't do it, but weeks on end of too low calories would be more likely to produce the effect-not a few days.
But-eating too low calorie causes other issues instead, such as malnutrition, and a higher risk for things such as gallstones. (Too quick weight loss is linked to gallstones-which is why many people, including my mother, have had issues, and gallbladder surgery from the popular crash diets in the 70's and 80's.)