If there are no other cars, people make them last. They are simple so easy to repair. They don't have many parts, so not much can break.
In the 1980 there were plenty of variations of Zastavas, Yugos, Fiats, Ladas, VW, Trabants, Citroens, Skodas, Varburgs, Renaults, Opels around.
While Yugo was certainly popular enough because it was supposed to be really cheap, I think I used to see a lot more Fiat 500s and Zastava 101 around back in the days. Yugo is just known more internationally because it was actually exported to the US.
The thing I remember about Fićo was its poor gearbox, where sometimes you had to hold it in gear to catch, and constant synchronizer failures. I also remember the Stojadin had a butter-smooth shifter that allegedly was a Porsche design :-)