No documentation and stated income mortgages are those provided by lenders without proof of income, such as pay stubs, bank statements, or tax returns. These types of mortgages were given to those with exceptionally high credit scores, to save time. These types of loans are no longer given since the collapse of the housing market. It was designed to make the mortgage process easier, because if you didn't have to provide documentation, you could come in, sign the paperwork and start moving into your new home sooner. No doc loans will usually always require a credit report and apprasial of the home to prove the borrower can afford to pay for the luxury/privacy of not having income verified and to ensure the home is valuable enough and in good enough condition for the loan.
They work well for people who don't consistently draw in a paycheck because they own a business, or for people who work on comission, or live off investments or other forms of income that are not well documented. They are a viable option for people who don't want to surrender their privacy to others. They are more expensive than other loan options, simply because there is a very high risk associated with them.
Stated income mortgages provide an annual income amount and list assets and debts. This loan type is usually for people who have more income than their tax return will show, because of high amount of write offs. Their income gives them the ability to pay the loan back, but with the IRS data, it doesn't appear to be the case.
The reason that no documentation and stated income mortgages present a problem is because without having to show proof of income, it is easy to qualify for a loan amount and payment terms you can't necessarily afford. When you can't afford the mortgage, it will eventually push you to foreclosure, which puts the lender in trouble. When enough of these loans are produced and enough people are no longer able to make the payments, you see a decline in the industry.