PMI (Private Mortgage Insurance) compensates the lender if the loan goes into default.
PMI provides no coverage WHATSOEVER to the buyer to keep their house in case of financial hardship that leads to the default.. But still the buyer has to pay the premium either directly, or in the case of "lender paid PMI - though a higher interest rate.
PMI adds very high additional fees to the borrowing costs when you have a meager down payment.
There are also additional underwriting requirements that the PMI company will impose on the loan.
This is the complicated part of the problem that some loan officers do not understand: The FUNDING lender can "approve' the loan, (subject to funding conditions) only to have the PMI company refuse to insure the loan against default. Since PMI is a funding condition, the loan does not fund.
I bring up this uncommon (but not rare) scenario because PMI companies are increasingly wary of stated income loans these days. Make sure your loan officer checks the stated income application with the PMI company underwriting criteria as well as the funding lender underwriter, early in the process