Short Sales Question


I’m new to real estate investing. Can anyone here answer this one question I had after reading about Short Sales?

If an owner have hardly any equity in a property, wouldn’t that person had to buy PMI when they took out a loan to buy the property in the first place? Therefore, the lenders has insurance in case of default (top 20%). Why would any lender sell a property short if they can foreclose and then claim PMI insurance? Wouldn’t PMI cover most or all sales shortages?

Thanks in advance for answers to my question!