Literally people born with or contracting disabilities that leave them permanently destitute due to you not being able to eat or house yourself without work you can't do because your disabled.
The simple fact of the matter is that most things most people do are simply input -> biology happens -> output. Breaking that hardwired process that happens in the background for every miniscule decision you make is the basis of like, every kind of therapy, self-help, meditation routine, etc.
I'd file that under trauma. If there was no trauma caused by extreme poverty like; parent was a sexworker; watching a parent lose it all; emotional neglect; physical neglect; history of incarceration; generational drug abuse, it would be more unlikely they would succumb to homelessness. That said, you are right.
Generational poverty is also historically about racism. Now, that's changing but it's changing more because it's just getting harder to get out of poverty than it is because there's less racism...