We examine how trust is sustained in large societies with random matching, when records of past transgressions are retained for a finite length of time. To incentivise trustworthiness, defaulters should be punished by temporary exclusion. However, it is profitable to trust defaulters who are on the verge of rehabilitation. With perfect bounded information, defaulter exclusion unravels and trust cannot be sustained, in any purifiable equilibrium. A coarse information structure, that pools recent defaulters with those nearing rehabilitation, endogenously generates adverse selection, sustaining punishments. Equilibria where defaulters are trusted with positive probability improve efficiency, by raising the proportion of likely re-offenders in the pool of defaulters.