At least in the US your race is stronger indicator for being incarcerated than your affluence levels. E.g. Black Americans are somewhere 10-30x more likely to be arrested for violent crimes than Asian Americans of similar poverty levels. Race here, similarly to economics, is again a confounding variable for something else that is actual causal to this. https://academic.oup.com/qje/article/135/2/711/5687353 . And again, the direction of causality here isn't obvious either.

Most likely it's a combination of genetics, cultural expectations, social support networks, and a litany of other elements that all come together to affect the ultimate outcome. Which aligns with your thesis around one's support network making a huge difference. But it's just important to point out that poverty by itself is not causal of crime, it simply makes it more likely given many other factors such as culture and community. It's mildly predictive, but up to a point.

Funnily enough, as a side-note, the stats show that most white-collar crime is committed by well-educated and affluent white men in their forties or older, causing a lot more financial harm than your everyday street crime added up.