Many races do have cash prizes. For a smaller race, it could be just a trophy, or a trophy plus something from a sponsor, but it could also be cash ($50-$100+ range).
I'm an avid runner. I can say with confidence there's next to no money in running if you're not a unicorn in the elite circuit. I follow the sub-elite scene moderately closely I'd say. The successful ones who are at it full time and have a sponsorship may live in a house or condo not much bigger than a shack. Some live out of their van.
There was a famous example of cheating (using EPO) a few years ago.
"In that time [roughly two years, I think], he won nearly $40,000 in prize money in more than 75 races, including international competitions, United States championships and local road races."