In the Heretic system, after failing the neurohack quest given by St. Josephine's mission enough times you can break the Neurohack ROM, preventing you from completing the quest. However, the quest does not fail, and will stay active. This prevents other stations from giving you their quests as they will tell you to return once your task is complete. Returning to St. Josephine's Mission results in them telling you that you've not yet completed the quest, but will not end it. The only way I found to end/fail the quest is to destroy St. Josephine's Mission.