That culture exists mainly in your imagination. Around 80 percent of the homeless are that way temporarily and will eventually be rehoused. The other 20 percent are chronically homeless and usually have problems that prevent them from being housed. But even most of those have been successfully housed by cities that have adopted a "housing first" policy, and it actually saves money. 

The homeless are as varied as the housed. The only thing they have in common is poverty, not having enough money to get into an apartment. The problem is growing because of high rents and low wages.

People who want real information about Eugene's homeless can find a useful summary at:

http://www.lanecounty.org/departments/hhs/hsc/documents/press_release_2016_pit_count.pdf