Where do I find these sleepy bullets? Mine always start wandering off further and further as the distance goes up. Maybe its because I'm shooting a little 308 and they get bored on their slow journey way out there, and start wandering off in a fit of A.D.D.? I'll have to see if the same bullets in a 300WM have enough attention span to get to the target.
Seriously though, physical impossibility. Lets just start a hypothetical scenario here, and say that bullets can be unstable and then stabilize after 100yds. In reality, some bullets might need some time to stabilize after they exit the barrel, given the right set of circumstances, but this is in feet, not in hundreds of yards. But for this case, lets pretend.
So lets say we have a bullet that is unstable until at 101 yards. It deviates to a 1.5" group at 100yds. Then, lets say it stabilizes at 101 yards and flies perfectly straight for the rest of eternity. We would have a 1.5" group all the way out as far as we wanted to shoot. But it still wouldn't be tighter than 1.5".
Add in the fact that I think everyone can agree that we will NEVER get a perfect bullet flight. So we would still expect some deviation after it was perfectly stabilized at 101yds, so it should still open up SOME as it goes out even if it perfectly stabilizes. Right? Nothing will be perfect as it travels another few hundred yards.
Now. To make the group smaller at a given further distance (linearly, not angularly for this argument, though both are true here), we would have to have a water-in-to-wine type miracle. Because not only would we need a perfect flight from 101yds out, but we would actually need some sort of a reverse trajectory force pushing the bullet back towards the center. It was already heading away from the center, something needs to move it back in towards the center, rather than on the straight path from the 1.5" spread. Right? So lets say the bullet is not stable, and it is 'wobbling' so to speak throughout the path. It would be a huge coincidence if that wobble was off at 100yds and brought it back in at longer ranges the exact same amount and distance it was off before at 100yds.
Now. Lets talk about those that say "AFTER xxx yards it will group". SO now we are talking about an additional force needed. The first described above, to move it back towards the center of the target at further ranges, and an additional force to square it up to the flight path and keep it there as it goes out to max range. Its headed away (1.5" @ 100), we push it back towards middle (to tighten the group), but unaltered it would just keep going past center as it traveled. Something needs to stop it right when it is back at the center and put it back on a straight path for it to be precise at all ranges past a set distance.
Hopefully this sheds some light to those that think this is possible. It was meant to show just what kinds of things you would have to concede in what you know about motion from every day life to make this possible; just throw them out the window.
When in doubt, question the human element.