While DNA:RNA hybrids contribute to multiple genomic transactions, their unscheduled formation is a recognized source of DNA lesions. Here, through a suite of systematic screens, we rather observed that a wide range of yeast mutant situations primarily triggering DNA damage actually leads to hybrid accumulation. Focusing on Okazaki fragment processing, we establish that genic hybrids can actually form as a consequence of replication-born discontinuities such as unprocessed flaps or unligated Okazaki fragments. Strikingly, such "post-lesion" DNA:RNA hybrids neither detectably contribute to genetic instability, nor disturb gene expression, as opposed to "pre-lesion" hybrids formed upon defective mRNA biogenesis, e.g., in THO complex mutants. Post-lesion hybrids similarly arise in distinct genomic instability situations, triggered by pharmacological or genetic manipulation of DNA-dependent processes, both in yeast and human cells. Altogether, our data establish that the accumulation of transcription-born DNA:RNA hybrids can occur as a consequence of various types of natural or pathological DNA lesions, yet do not necessarily aggravate their genotoxicity.