In a number of genera, the mollusc disolves the inner shell wall as it
grows.  In Conus, it is easy to see this process.  The inner walls are
very thin.  The inner walls are also very smooth, so it wouldn't appear
to be a grinding process.  Also the Conus radula (a barb) isn't suitable
for grinding.
 
As suggested, presumably the mollusc uses the dissolved material in
adding new shell material at the lip.
 
Aloha,
 
Wes