What makes you think that poor people don't inherit property? There are lots of people with very low incomes but who own a house. And no they don't just sell it. Why sell the only house you have? Or maybe it is not their house but it is a piece of property that they have always owned and which they use as a garden or a yard or storage.

They don't sell it because they'd rather have a piece of land to enjoy then some money in the bank. It might be their only luxury in an otherwise frugal life.