This isn't 25 years ago. I just got rid of my 12 year old car that had a blue book value of ~$1000. It wasn't the prettiest thing, the trunk latch needed a bit of fiddling to get to open as the spring in the external latch handle was worn out, it leaked oil (slowly, about a liter per month) and it had a few other minor issues with it, and someone had backed into the driver's side door in a parking lot, leaving a dent about the size of a dinner plate. I traded it in, but if I sold it privately I realistically would have gotten about $700-$800 for it on the open market based on comparables for sale in the paper and on Craigslist at the time.
The reason I got rid of it wasn't that it was unsafe or it wouldn't start or run, it was that to bring it back to 100% would cost a couple of thousand dollars that I figured would be better spent getting something newer and fancier that I can afford to do. It was still mechanically sound aside from the small oil leak and pretty much the most dependable car I've ever owned. If selling it privately wasn't such a hassle, I would have been happy to see it go to some college student or other person who needed good basic transportation for not too much money.
There are lots of cars in the $1000-$2000 range these days that are sound and dependable, their only sins are that they are old and cosmetically challenged.