If you default on your mortgage for a few months you get an option to do something called a "loan modification". If you qualify, they'll change your rate.

In order to qualify you have to declare net worth, find pay stubs, and a whole lot more stuff.

Your rate will go down but your credit will get hit hard for not paying your mortgage.

I work at a company that deal directly with borrowers on matters like this. Let me know if you have questions.