It is a common misconception that Lenders Mortgage Insurance protects a borrower. It does not. It protects the lending institution.

In Australia it is common for banks to insure any loans over 80% of the value of the property. The reason for this, is as the loan to the value of the property increases so does the risk to the lender.

As an example a property is worth $500,000. The first borrower borrows only 50% of the value. At $250,000 if the borrower was to default, then the lender has less chance of incurring a loss, as there should be $250,000 worth of equity. It is highly unlikely the property will drop by 50%, however it can happen.

The same property worth $500,000. The second borrower borrows 90% of the value. At $450,000 if the borrower was to default, then the lender has a large chance of incurring a loss, as there should be only $50,000 worth of equity. It is quite easy for the property to drop by 10%. For this reason, most banks mortgage insure over 80%. The higher the ratio, the higher the premium, which is normally passed on to the borrower.

for how it works in the USA here is a good link to Wikipedia