If there be no soul or transmigrating entity that takes rebirth, who or what bears or enjoys the consequences or fruits of karma?

How can a religion or school of thought justify or rationalise the proposal that potential suffering could be inflicted on a subsequent rebirth - to all intents and purposes, a new individual, according to the anatta theory - because of the actions of a previous individual? Why the threat of subjecting another to suffering, if that being cannot be held responsible for actions in a previous life? If no soul or persistence exists, how can one suggest that performing positive karmic actions will improve the quality of life of a subsequent rebirth, if there is no element retained of a previous iteration to reap the reward and receive the incentive to continue to perform good karmic actions and/or continue in Buddhist schooling?