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When you become poor, a beggar's mentality emerges.
Literal
Poverty-do [when-と] beggar mentality [subject-が] comes-out.
貧乏する is an unusual suru-verb meaning 'to be/become poor.' The conditional と marks a habitual consequence — 'whenever X happens, Y inevitably follows.' こじき根性 ('beggar mentality') is a harsh compound: こじき (乞食, beggar) + 根性 (deeply rooted nature). The saying suggests poverty breeds a debased mindset.