Poverty [because-of-のために] people [topic-は] sometimes crime [object-を] committing [sometimes-happens-ことがある].
のために here is causal ('because of'), not purposive. 犯罪を犯す ('to commit a crime') is a standard collocation. ことがある in its habitual sense means 'it sometimes happens that' — distinct from the experiential たことがある.