Supplies of any raw material are mostly governed by economic factors. For example, as demand goes up for a given quantity of supply, the price increases. This stimulates manufacturers to increase their production of that supply, I.e., to dedicate more resources to finding meerschaum or growing briar. So there is no static stock of each that simply runs out. It’s a dynamic system.
As for the stock of meerschaum in the ground, no one knows. Until the price of meerschaum goes high enough to warrant searching for deposits, we just only know what deposits are currently found and being used.