Here's my thought:
You had at least two important groups of Terrans during the Interstellar Wars period. One would be the Terrans who embraced the Confederation with its unified world government and their we're all in this together perspective. While the other group would be the emigrees, groups that for cultural or political or religious reasons wanted to hang on to their individual identities and had no interest in giving up their heritage for Anglic lessons and a vote in the united world congress.
The latter group explicitly settled outside the Confederation borders. They didn't care how the Interstellar Wars went.
A subset of the former group, which embraced the Confederation, thought that the best way to ensure the survival of the Terrans was not by fighting the Vilani, but to expand as far and as fast as possible. They planted colonies as quickly as they could wherever the Vilani weren't: to spinward, to trailing, to rimward.
But these Confederation colonists had less than 200 years to explore, settle, and put down roots. By the time most of those new colonies had just started to take shape the Interstellar Wars were over, and the Rule of Man had begun. So the "big border" is really just a paper tiger, more empty space and barely surveyed systems than fully developed, mature colony worlds.
I'm sure plenty of the Confederation colonists had no interest in joining up with the Second Imperium. They stayed right where they were but declared their neutrality after the coup.
But I'm sure plenty more colonists saw much easier pickings on the old Vilani worlds to coreward. Given the choice, would you try to scratch out a meager living on a harsh new world, or would you rather move to an established, comfortable planet where you would become an automatic aristocrat?
So I think what happened was that a lot of the new colonies were abandoned almost overnight, while others simply refused to join the Rule of Man. As a result, the rimward borders collapsed, leaving behind a relatively limited number of worlds that had been settled by Terran Confederation colonists.