LAS VEGAS -- Eddy Buompensiero noticed eight pairs of shoes outside the door of the modest house on Mother of Pearl Street, evidence that the former owners were still living there even though the bank had foreclosed.

Mr. Buompensiero, a gray-bearded inspector for REO Asset Services-1st Realty Group, rang the bell. When no one answered, he taped a letter to the door offering the occupants $1,000 to move out. The catch: They won't get a cent if they trash the house before they leave.

"If...