Emerald Crab in Reef with Trumpet Coral?

No crab is 'safe', they're opportunistic. That said, your EC may be picking at dead/dying flesh if the coral is on its last legs. I'd move either the coral or the crab if you want to save the caulastrea.
I had a pink mithrax that was fine for a while, then ate corals after his last moult. After I evicted him, I bought a tiny green female EC and she's a model citizen - she won't even take pices of shrimp from me, she'd rather pick away at algae. She cleans all around the corals, but leaves them (and the sponges, tunicates and macro) alone in favour of the bits of microalgae she finds.

The bigger emeralds (or any crab for that matter) get, the more risky they become for your reef. My green guy got nasty a few months ago after over a year of being docile.

The only "reef-safe" crab I've come across (so far) is the porcelain crab mainly because it stays small and is a filter feeder rather than a detritus picker.

:coffee2: yes, emerald crabs can be bad. mine pick on bubble coral and pollips. I gave away the pollip one and still trying to catch and give away the one that likes my bubble. do not listen to anyone who says that emerals crab is reef friendly.