I don't think there is all that much mystery in it, though the mechanics of it are somewhat murky and no doubt the result itself was distinctly unanticipated by Napoleon himself.
What is really operating is pre-railroad logistics limitations. There is a reason armies of 600,000 men are not encountered in history earlier. They don't work. Not until iron horses can deliver hundreds of tons a day in supplies, at will.
See, a typical army in the age of muscle power was limited in overall size, above all in the size operating as a single body, by inherent logistical limits set by muscle power on the one hand, and the typical density of food and fodder per unit of settled area on the other. There is a pretty hard limit at around 100,000 men. Above that you can operate briefly, if you have magazines or water transported supplies. Otherwise you start evaporating, and the farther you are above that level the faster you melt.
There is only so much food within a day or two's march. You need to gather hundreds of tons per day. Horses or oxen can help fetch more from farther away, but eat their own load weights in fodder in a relatively short distance. If there isn't fodder for them or they are overworked, they die themselves (and are eaten by the hungry troops). Napoleon's earlier armies are down in the 50,000 to 100,000 range. Army corps are meant to maneuver separately in part to avoid overtaxing a given forage area, and are only 25,000. Those can live off the land indefinitely, if the land is reasonably developed and it isn't the depths of winter. Brief concentrations for battle - days - are OK, make no difference.
But you can't push above 100k for weeks without eating out the entire countryside within forage distance of the column. And as soon as you do, if you don't stop or disperse, your horses and cattle start dying, which reduces forage gathering ability still further.
All of that would operate even in western Europe. But in addition, this was Russia, not Germany. And northern Russia - heavily forested and low population density at this time. There was much less forage than in western Europe, per average mile of march.
So what did they do? Men straggled because they were out looking for food farther than a day or two's march from the column. By the time they had found some and tried to return to the column, it wasn't easy to catch up. And its wake was picked bare. So men tended to radiate away from the column. At first not intentional desertion, just forage parties, then fed up and just looking for food, then having no intention of coming back.
Napoleon could not pause to gather them - the usual remedy for stragglers - because the main body would starve if it did not enter fresh forage territory. Above all, the livestock. The horses died much faster than the men, enough to impair the cavalry as early as Borodino. (Supply services give out first, battle cavalry last).
So what happened to all the stragglers? Some of them straggled out of Russia no doubt, before the crisis of the campaign. But many of them fell to the cossacks, either during the advance or while hanging around, scattered, that winter. Or even to local peasants. They weren't exactly paying for things and would have been treated as brigands.
Foraging parties smaller than infantry divisions would not have stood up to the cossacks, who roamed everywhere in brigade strength. (Notice, a few thousand irregular cavalry constantly on the move, can forage easily over a wide area. Not tied to anything, and able to reach many times the distance every day).
The numbers not in the side groups or the main column aren't dead in the fall, though a portion probably are. But not many of them are still alive by the end of the winter, and those that are, are either not in Russia, or have "gone native" (getting along with locals rather than fighting them - if they fight, next time cossacks come through they lose).
No doubt disease also helped, and for some of them simple starvation, wandering around the forests without maps looking for anyplace not vehemently hostile where there is food to be had.
The bottom line is Napoleon had nothing remotely like adequate logistics to support the size of army he gathered. Armies that large were not supply-able in that era anyway. He did not know it. He had used improvised forage for most of his supply needs - looting in other words - since Italy. But there was a lot less to loot in northern Russian forests, and a lot more men to feed than ever before. It was physically impossible. The core of the army continued on as ordered, eating their animals in the process, while the excess above the "carrying capacity" of the land melted away.
The force he was able to supply at Moscow, wasn't enough to withstand the force the Russians could still supply east of Moscow. So it all failed. Amateurs study tactics, professionals study logistics, the adage runs.
Actually, the theme you write about comes up today as well, in both Afghanistan and in Iraq. At some point, as we increase the force size, the logistics requirements require a larger and larger portion of the troops, and at some point, the addition of more soldiers can actually reduce battle strength.