A serious behavioural failure may be uncommon within a person’s history yet become the principal basis for judgments of character and future risk. This conceptual article develops the conjunctive misfortune problem: adverse conditions, culpable action, stochastic harm, categorical institutional responses, and persistent collateral consequences can combine to generate sharply divergent life courses. An interdisciplinary narrative review connects accident theory, Bayesian person perception, moral luck, criminal-record stigma, and digital punishment. The analysis distinguishes an event’s low predictive probability from its diagnostic value, and derives conditions under which outcome severity adds no character information once conduct and context are fully observed. It formalises biographical compression as loss of sensitivity to relevant history, separates that phenomenon from rational evidential updating and precautionary exclusion, and shows how harm thresholds and interdependent sanctions can amplify consequences. A dimensionally coherent burden model and a discounted collateral punishment multiplier make the amplification claims explicit without presenting a numerical measure of moral desert. Five proposed experiments distinguish historical-evidence weighting, resultant luck, contextual explanation, sanction interactions, and reputational compression. No participant data are collected and no empirical validation is claimed. The normative contribution is a principle of differentiated accountability: acknowledge wrongdoing and victim harm while requiring distinct, reviewable justifications for character inference, protection, reparation, and continuing exclusion. Rarity cannot establish innocence or proportionality; equally, serious harm does not establish that one observation exhausts a person’s biography. ( direct link )