These pictures were sent to the identification service - could it be a weird fossil insect? In fact it is not actually a fossil, but part of a modern crab - it is the abdomen that would be tucked underneath the crab in life. The appendages folded inside the abdomen are called pleopods, and these are used by female crabs to carry eggs. They are the same structures that shrimps use for swimming. A nice beachcombing find!