How many people are poor like that? And the amount of money they hold seems a poor indicator, too. People who have paid off half their million dollar house, and have an income of 20k/month would count as poor.
If the average household has 5k in savings, pool with your parents to get to 10k.
Or take on some night time job once per week, to earn an extra 400$ per month, and save for 2 years.
And you don't have to buy a whole house, a small flat can be a sufficient start.
I have to say I have never done this, but I was recently in talks with people who propose doing that and help people who do it. It sounded plausible - why not? You can buy a rented flat (that already has tenants who pay rent). So the numbers are pretty much clear.
They told me the bank doesn't count the rent as your income, though. That is the catch. So for your first investment like that, you have to be creditworthy on your own. However, after a while you can build trust with the bank (they see the rent from the tenants keeps coming on a regular basis), and get more credit. Then you can start the next project.
You don't have to invest in a desirable area, as you don't want to live there yourself.
Nevertheless, I am still not convinced it is for me. I worry too much about bad tenants, things breaking on the property and so on. I have almost no knowledge about housing properties (like to how do you recognize damage to the property before buying it, how much do repairs cost, and so on).