The thing about birds is that they don't chew their prey, they normally swallow it whole. Yeah, I know, there are a number of exceptions.
An old girlfriend re-habbed raptors, and even the tiny screech owls will eat a full grown house mouse whole. One Red-Tailed Hawk she had would eat a dozen at one feeding.
Anyway, maybe the tastier/easier to chew parts were the body of the crawfish and the predator thought the claws were more work to chew open that they were worth? Or it was a smaller predator (small mink or 'coon [YOY])and lacked the jaw strength to crack open the claws?