Significance We provide evidence that in organisms with gigabase-sized genomes, such as humans, one or more stretches of DNA typically remain unreplicated when cells enter mitosis and are segregated to daughter cells via structures called ultrafine anaphase bridges. p53-binding protein 1 (53BP1) accumulates at the subsequent DNA structures inherited by each daughter cell in the following G1 phase to facilitate resolution in S phase. We show that the abundance of these structures match theoretical predictions for the number of unreplicated DNA segments when the number of replication origins is artificially increased or decreased. We show that 53BP1 preferentially binds to chromosomal regions with low numbers of replication origins. This work challenges the prevailing view of how genome stability is maintained in proliferating cells.