When you finance a home, the Lender keep some money in your escrow account for property taxes and insurance of that property. And yes, even when the homeowner stop making the mortgage payment the Bank still have to pay the property taxes and homeowners insurance.
Of course is possible. You need to get some store credit cards, buy small items and pay right away.
This will appear in your credit report on the next 60 days and your credit score will go up. In the other hand, you should shop around for a mortgage broker that can explore your financial options and advice you.