The "Very Bad Thing" is a terrible event that occurred in the aftermath of World War II that was so heinous that Joy was invented to block out memories of it's existence. Very few people in game that aren't mad or wastrels recall the event, and causing someone on Joy to remember has been shown to cause hospitalization due to shock.
Through Arthur's story, it is revealed that, several months after the German Empire conquered Britain, the Germans gave the English an ultimatum: hand every single child (except children 13 years or older) over to the occupational authorities or have their cities obliterated by a special Tiger Tank division. Eager to save their country, the remains of the government agreed, and thousands of children were ripped from their families and forced into cattle cars on trains to be shipped away. Unfortunately, years later, after the Germans left to fight the Soviets, the government discovered that the tank divisions left behind were made of paper-mache, meaning that England had been fooled into giving up children as hostages. Terrified of what might occur if the common people found out, an army camp was built around the "tank division" to scare away prying eyes, a historical revision organization was founded, and funding was put towards the creation of the mind-altering drug Joy to prevent anyone from remembering the truth.