Its nice to see a variety of answers. Eric's response is possibly the closest to what will happen.
The basic flaw in the situation painted by you is that the moment the owner quits claim to you there will be an acceleration of the loan or due on sale clause. The entire mortgage will have to be paid. Remember, the mortgage is not a lien on the owner but on the property. Either the owner or you would have to pay the $525,000 mortgage back to the lender. If you'll can't, the lender forecloses on the property. And with that there goes your $37,236