The primary problem with government subsidies and assistance is that you are paying money to people/corporations/whatever for making bad decisions. You cannot eliminate a problem by rewarding it, at any level. When your child takes all of his allowance money and loses it after investing in a scam or gambling with friends....do you replace his allowance, or do you say, "Gosh, that was a really bad decision. I'll bet you don't make that mistake again." When a child skips school do you do his homework for him and excuse his absence...or even better, attend his classes in his place? No, of course not, because that is rewarding bad behavior.
So if people come into this country illegally, or they have children out of wedlock, or they become addicted to drugs, or they enter into ill-advised mortgages...why on earth would we suspend our good sense and give them money?????
The money is going to the mortgage companies, not to the buyers. The buyers aren't receiving any money.