Is such a thing even to be had these days? I certainly own a decent $6k car, so I know it used to be possible. But I bought that car 14 years ago now, and it would surprise me if you can still get a decent car for that price after 14 years of inflation.
I bought a $4k car a couple of years ago. It’s had a few issues but nothing I couldn’t handle in my garage with fairly common tools. I’d say you can still get a very good car for under $10k and much less if you are handy with wrenches.
When shopping for this sort of car look for private sellers. Used car dealers in this price range tend to be sketchy and none of them do any maintenance or repairs before the sale.
Yes, I think the private party seller comment is right.
I had to sell a decent 15 year old car due to upgrading two years ago for less than $4K. It was a decently reliable car and I think they got a deal. With these, I think you can good deals if you don't mind the downsides. Reliable-ish, with one bigger problem (e.g. AC doesn't work, or has some crash damage), and no guarantee of how long it'll run or when it'll need bigger work (could be years and 50K+ miles, or sooner).