Any cobblestone slabs that are stored away in chests before update 1.11.0.1 have been turned back to normal cobble but still keep the name "cobblestone slab" you can use them to craft anything. When placed it looked like a cobblestone block but when you break it it turns into cobblestone slabs
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It sounds to me like the slabs in your inventory were converted into double-slab blocks. They look just like full cobblestone blocks, but internally they have a different identity and won't stack with real cobblestone. You also can't use them in crafting recipes that call for cobblestone.
To check whether you have double-slab blocks in inventory, try placing one and re-breaking it. If it turns into slabs, it was a double-slab block. As a workaround, place and re-break all the double-slab blocks in your inventory. You should only have to do this for slabs that were in your inventory when you upgraded, and only once.
So far, there have been no reports that the bug affects slabs stored in a chest or other container before upgrading. If anyone has seen that happen, please tell us below.