Can housing Authority collect income if you are self employed collecting cash ?

From a Housing Authority website:

Housing fraud is any action or failure to act that allows a Public Housing tenant, Section 8 Housing Choice Voucher Program (HCVP) participant, or HCVP landlord to receive benefits for which the person doesn't qualify. A person who knowingly withholds information, fails to report a change in the family's circumstances, or otherwise engages in activity prohibited by program regulations, is a benefit thief--stealing benefits from families in need who legitimately qualify for them.

The vast majority of families receiving housing assistance from HACA, and HCVP landlords, are honest and follow program rules. Regardless, HACA is committed to the integrity and effectiveness of its housing programs and operations. This includes preventing, detecting and prosecuting waste, fraud and abuse when it does happen – including by using tips, whether self-identified or anonymous.

You could do anything.....if you want to lie your way thru life. Be honest. you will NEVER get in trouble if you tell the truth. And you'll respect yourself a lot more for it.

I'm not sure I understand.
You want to live in public housing for free while you save money to buy a home?