HUD could catch this type of fraud simply by running a credit report on each borrower.
HUD is a money laundering operation, they haven't submitted an audited financial statement in years.
There's a lot of complicity on different levels - the banks and HUD are looking the other way, accountants are falsifying tax returns, agents (who might be illegals themselves) are likely overseeing and directing the whole scam. I've heard of illegals who have developed a good credit history actually renting out their SSN (and therefore their credit history) so that someone else can use it to buy a home.