As bfuller already said, they do exist. I got my 2005 Honda Accord (Manual) on craigslist (2 days of research) for $2900.
It has lasted me 5.5 years now with no maintenance except oil changes.
I've noticed manual transmission cars are usually discounted relative to autos.
Possible that you got lucky in a lemon market?
It definitely does, you just have to be willing to spend the hours to look for the deal.
FWIW, I bought a 2004 Corolla with 140k miles off Craigslist in a HCOL city for $3,200 back in June. No issues so far.
Look for any 1999+ Toyota Carolla/Prism with under 200k. Many camary of that era are bulletproof. Civics all got bought up by ricers, but '3k civic' is literally a meme for being so common.