The people who are ACTUALLY poor, don't have such things.
It's very common for people living in traditional working-class neighbourhoods to own a house and suddenly become paper rich when gentrification happens (e.g. Venice Beach in LA). They might find themselves in a situation where, in theory, they have a lot of wealth from the house but don't participate in the economy at the same level.
There are homeless people.
People who are barely able to rent a room in a crack house.
You are NOT POOR if you own a single family house in Englewood. End of discussion. Sorry.
Sell your house and live off the annuity for life at > median income after taxes in perpetuity. If you don't, there is literally no excuse for your situation other than your own choosing.
What's different here - that is critical - the actual poor HAVE NO CHOICES.
And for those who will say, "Then the government should just build more houses", let me point out that we might run out of space before the appetite for real estate investment dies out.