If you receiving HUD housing, can you collect rent from someone who is living on the property that you have inherited with other family members? Is this illegal

I am not sure what you are saying the circumstances are but with HUD sect 8 you are not allowed to rent from family. From what I can make of your question it does not sound legal at all.
If you are saying they were joint heirs and they receive HUD rent payments, the forms the renter has to fill out specifically ask what assests/properties you own. They very likely are not truthfully informing HUD of their situation.

You will have to report all income to see if your qualify for the housing assistance.