It's too bad. My in-laws were members until recently and I've played Briar's Creek a whole lot over the past 10 years. It's a really neat place and a really first class set up. I don't think the course is as good as the private options on the nearby Kiawah, but there are a bunch of good holes, it's always in perfect shape, and it's never even remotely crowded.
I have zero knowledge of what happened here, but my best guess is that the club was tied heavily to selling high-end real estate on the property on and near the course. The biggest problem with selling lots there is that it's next to Kiawah Island...which has a number of advantages (access to the beach, closer to Freshfields, etc.) than Briar's Creek.