Electricity bills. Speeding tickets. Dentist records. Money order receipts. The search for documents is on for immigrants who may qualify for a work permit and reprieve from deportation under measures President Barack Obama announced last month. Applicants must prove they were in the country continuously since Jan. 1, 2010 — a tall order for many accustomed to avoiding trails. For critics, conditions are ripe for fraud.

President Barack Obama unveiled one of the most sweeping changes to the U.S. immigration system in decades, shielding millions from deportation.

For a company that booked $12 million in annual sales importing snacks like chile- and lime-flavored chips from Mexico, Baja Distributors Inc.’s offices were oddly quiet. There were no signs outside. Its small warehouse was almost empty. Phones went unanswered.