That's a very good question. Being proactive would be one solution. If the names of the people the government sent out payments to are already in the database, the government could send each person a letter of intent stating that, according to government records, they received money. The letter could say something along these lines: “Please be advised that, within the next two months, you will be receiving an information slip indicating that the amount is taxable. If you disagree with the information, please contact us.” That approach would be much more proactive than reactive.
Another important thing to remember is that, very often, the money is deposited into accounts the fraudsters open up in the individual's name. Victims who receive the letter will realize that they never collected the benefit and will alert the government.