How does Buddhism avoid the problem of karmic misattribution across lives without an unchanging substrate consciousness?

In Buddhist doctrine, the teaching of anattā denies the existence of a permanent, unchanging soul or self that persists across lifetimes. At the same time, Buddhism maintains that beings are “heirs to their karma” and that intentional actions in one life condition experiences in future lives. Canonical Explanations of rebirth describe this continuity in terms of causal processes, such as dependent origination or a stream of conditioned phenomena, rather than the transmigration of an enduring entity. In other other philosophical systems that believe in reincarnation, take hinduism for example, rebirth is explained through the concept of a subtle body (sūkṣma śarīra) that survives death and carries karmic impressions (saṃskāras) across lifetimes. This provides a mechanism for why the karmic results experienced in a later life belong exactly to the same individual who performed the actions earlier. Buddhism rejects the existence of such a persisting entity. Rebirth is usually explained instead as a causal process (often compared to one flame lighting another). However, this raises a difficulty. If there is no enduring self or carrier connecting the two lives: In what sense is the person in the next life the one who experiences the results of the earlier person's karma? Why would this not effectively mean that the karma of one person is being experienced by another? In other words, without some form of persisting substrate that carries karma across lives, what prevents karmic results from being morally misattributed between different individuals? More broadly, if there is no persisting subject that carries karmic responsibility across lives, would this not make the operation of karma appear morally arbitrary or unfair?