During World War II, Switzerland's restrictive refugee policy is starkly illustrated in "The Boat Is Full," a gripping drama that follows six individuals from different backgrounds as they attempt to seek asylum in a small Swiss village. Led by Judith Krüger and the deserter Karl Schneider, the refugees pose as a family with children, hiding their true identities from the local authorities. As the story unfolds, the group's fragile deception is threatened by chance encounters and the relentless pursuit of the village policeman. Will they be allowed to stay, or will they face deportation?