Actually I am an archaeologist but have a good geology background. Sounds like a silica based rock. Such as forms limestone. You said it is found in caves? Over time with the right heat and pressure clay can slowly turn into a rock. That the center is still soft means the outer layers have hardened but the core didn't have the right conditions to finish the job. Looking at the outer shell I would also venture that there was intense heat such as from forest fires that fused the silica. Clay, etc has a platelike structure so a whole layer has become exposed. Since there are lots of squarish "rocks" I would say the plate dried out and broke (like you see clay crack when it dries out in the sun) before it was subjected to heat. That would create the shells. I will have to check out the geology of your area to know for sure.
