Is it possible the jar is a match jar jar? The stone for striking? It would be a bad design but I have seen worse. Or perhaps a cigar jar?
Does the cork have any lingering scent? Or the stone? Either one would have some odour from its original contents.
I agree with both dave and rj, I would not use the stone as a humidifier, both the stone and cork can easily moulder, especially if they have previously been innoculated with mould spores. Bag line it.
Does an 8 oz tin fit inside it? Or possibly a stout tobacco tin from the 50's to the 80's? That may explain the cork lining. It would not surprise me if it was made to house a plug-style tin with the lid removed to make it less a nuisance to access tobacco. With a rubber seal and a wetstone there would be no need to replace the plug in the tin each time.
Curious piece, nontheless.