Possible Clues:

• It's raised before the start of a play
• Agatha Christie novel subtitled "Poirot's Last Case," or what can follow the starred answers' last words
• One's often high during a performance but down after the show
• Stage feature
• Poirot’s last case
• Hanging pawn's last after sharp champion
• Drape's kin
• Almost cut short new hanging
• Maybe blind dog following has run away
• It hangs between audience and stage