First off, usually ships sell out (especially RCCL and the CCL Glory which are in N.O.), and when they DO have rooms open, they dont sell them at a discount, they sell them at a PREMIUM!!
Typically when they have a cancellation, they get all the money that the person paid, so they are not losing anything. So they would actually SAVE money if you didn't go (less food, etc). So they usually sell cabins at the FULL TARIFF rates which is Brochure prices (which NOBODY PAYS).
Don't try this. What you CAN do is try to see if there is a cheap deal a week or so before hand on one of these ships (hoping they are not sold out).