I'm not a big 'coral' guy, but I have seen this happen / have had this happen many times. It's never been an actual problem, per se. Someone here can probably provide a more thorough explanation as to why. ;)
Some branches look like they might even fall off soon due to how thin they're getting around the "strangled" parts.
It seems to be acting as it normally does (shrinking down at night, growing back up during day), almost unphased by the fact that it's on the verge of amputation. But overall looking sicklier with time.
All-in-all it's a pretty good size coral, and looks healthy. "If" a piece drops off, pat the bottom dry and use superglue 'gel' to cement it to a dry frag plug, and Ta-Da!... you're a new Dad. ;)