There is a brief discussion of this process in Vermeij's A Natural History of
Shells, but I don't have the book with me so I can't cite the page numbers.
If I remember it correctly he says that either the spines, etc., are absorbed
or they are placed in such a way that they will be out of the way of the
growing shell. However, he doesn't indicate how a snail dissolves its own
shell. I suppose they use an acidic secretion, something with HCl in it. Or,
perhaps they scrape it with the radula. The latter is the method land snails
use when consuming calcium carbonate containing substrates.
 
What do the snails that drill their preys' shells use, besides the radula?
 
A.