General:
* Impoverished
* Destitute
* Indigent
* Needy
* Deprived
* Underprivileged
* Hardscrabble
* Wretched
* Miserable
More specific:
* Chronic (referring to long-term poverty)
* Extreme (referring to severe poverty)
* Absolute (referring to the lack of basic necessities)
* Relative (referring to poverty compared to others in a society)
* Generational (referring to poverty passed down through generations)
* Urban or Rural (referring to poverty in specific areas)
The best adjective to use will depend on the context and the specific type of poverty you are describing.