If you're facing homelessness, then perhaps buying a home shouldn't be your top priority. Your top priority should be to find a stable housing situation. And that more likely means renting than buying. Check with your county's housing office, or your case worker, to find a stable housing situation.
Just for the record, sure, you can buy a home for less than $6,000. Plenty of mobile homes sell for less than that, though you'll also have to pay ground rent.
Or you can buy a property "subject to" an existing mortgage. You get the deed, sometimes for no money, sometimes for a few thousand. But then you have to make the monthly mortgage payments.
Or you do an equity share with someone with the necessary downpayment and credit.
But in your case, the question isn't one of finding a house to buy. It's finding a stable place to live.