If you look at some of the other bullets in that last picture you posted you can see on several of the traditional FMJ bullets the cores are starting to separate too. They just didn't peel completely apart.
That sandstone backstop is working about like a ceramic trauma plate in a bulletproof vest. It is brittle enough where it will shatter and absorb a lot of the bullet's energy, but as you noticed, it's not trapping the bullets. They just fall to the ground after all the energy is expended...or bounce back a few feet.
I hope you're shooting at an oblique angle to it so any of those rebounds are most likely to head in a safe direction.
My backstop down at the farm is a big shale/gravel bank that we have dug out for use as fill. Those small rocks, sand, and shale do a good job of boogering up but still capturing the bullets. I'll get the occasional ricochet if I do smack a small rock at the wrong angle, but most of those have been screened out from the pile that I usually set up my target butts by.
I have picked out a few bullets while loading out of my pit too...a lot of my "plinker" FMJ .380, 9mm, and .45ACP will have separated. JHPs and other soft-nose bullets usually hold together better. I wonder if it's because in a FMJ when it impacts something hard and the jacket deforms, the lead core has a tendency to get pushed out the opening in the back. While on a JHP/JSP the core is being pushed farther back inside the jacket.