I think a lot of people are overgeneralizing the dynamics of urban poverty from what they have observed in the last decade of home ownership trends, but affluent white flight from cities only really ended in the mid-00s-2010s (for some cities) and there are plenty of significant poor populations near urban cores able to remain because it's either where section 8 housing was built or by rent control.
They just take public transit or walk. Not biking.
You know how long the waitlist is for section 8 is, in say, New York? All poor people don’t just go out and ask for section 8 or rent stabilized apartments and instantly get them.
I think I likely know more about urban poverty than you do. It is incredibly hard to get a section 8 apartment, especially if you aren't a family, and it is becoming increasingly difficult to do that in urban cores as section 8 contracts are being shifted towards outlying areas.
Nonetheless, there are lots of people in urban areas living in section 8 housing and it is a substantial part of the story around urban poverty and how people still afford to live in urban cores.
They just take public transit or walk. Not biking.