The widow in Luke 18 repeatedly approaches a judge demanding justice against her adversary. Jesus deliberately describes the judge as one who neither fears God nor respects people.
The story therefore places a socially vulnerable petitioner before an authority who lacks both religious and social motives to help her.
Widows could face economic and legal vulnerability when they lacked strong male kin, though their circumstances varied. Biblical law repeatedly commands justice for widows precisely because they could be exposed to exploitation.
Judges were expected to render justice impartially. Jesus' judge is defined by the opposite disposition. The widow apparently has no bribe, patron, or status with which to move him; she has persistence.
The social imbalance makes the parable's comparison powerful. If even a corrupt judge can finally respond to persistent appeal, God's willingness to bring justice for his people should not be measured by the character of that judge.
The widow models perseverance precisely because she continues when the human power structure gives her little reason for confidence.