PMI may want the house back following a foreclosure, in order to attempt to recoup any loss they may have due to a claim. In that instance, they may not approve a short sale.
PMI will often approve a short sale if the market indicates that they have no shot at recouping their loss or claim. Or often, there is some middle ground, whereby the Lender could sell it for 85 to 90% of the original loan amount, thereby reducing any such claim to PMI. Much like any foreclosure and dealing with Loss Mitigation, each case is different... not sure why, maybe it is the Rep you deal with, the latest whim of mgmt based upon their recent losses, et al... Those policies change all the time, so the best thing to do is ask... and see what they say.
If a borrower defaults on his conventional mortgage (goes 90 days late on a payment), the lender files the foreclosure notice and sends in a claim to the insurance company to recover as much as 20% of the mortgage balance. This, in turn, gives the lender a smaller risk when the lender sells the property to recover their losses.
Let's assume we have a $300,000 loan for a property that was purchased last year but now being sold via short sale for as little as $260,000 today.
How much will the lender receive from the insurance company?
$300,000 times .20= $60,000
What price must the lender sell for to not have a loss?
Well, the lender's exposure has been limited to $240,000 now that they received $60,000 from the mortgage insurance company
hope it helps.