The short answer is that you lied and if they find out, you could be prosecuted.
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Woudl be charged with welfare fraud. Before you try and change the information you need to talk with a local criminal defense attorney.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
I agree with what has been said but would add that there is an old saying "the Wheels of God grind slow but exceedingly fine." Never assume that you can cheat the government, your act will have a way of catching up, and you could suddenly find yourself having to defend yourself in a years old case.