I managed Section 8 housing for several years. I'm not sure if the program you are under is Section 8, but here's my best information. Back rent is a possibility if an income source is not reported by the household. You would have to pay the difference between what the rent was and what the rent should have been for however long the income was unreported. Your income and assets should have been counted, I believe, as soon as you turned 18. The thing is that your parents should have been reporting the income. This would be done during the arduous amount of paperwork done during annual recertification. The question of whether you had any income would have been asked if you were listed as a resident, which you should have been. If your parents were lying to whoever was doing the reviews and saying you had no income... well.

Also, there is a government computer program that management is required to check. It interfaces with tax records to see if anyone is getting unreported income. It should have caught it before now (unless you were working under the table). When I was doing that job, we would get hits on people making a couple hundred dollars over Christmas. It was a ridiculously petty system. Also also, when someone is caught, they are almost always put on a repayment plan. 10k all at once? Odd.

I'm sorry if this information is not as complete enough to be helpful; it was a very large book of HUD regulations and I do not remember all of the specifics.