Many people were corrupted by drug addiction.

Literal

Drug-addiction [by-で] many [possessive-の] people [subject-が] were-corrupted.

堕落する ('to become corrupt, to degenerate') is a strong word — 堕 ('fall') + 落 ('drop'). で marks drug addiction as the cause of the corruption. した (past tense) frames this as a completed historical observation.