Lytic herpes simplex virus 1 (HSV-1) infection triggers disruption of transcription termination (DoTT) of most cellular genes, resulting in extensive intergenic transcription. Similarly, cellular stress responses lead to gene-specific transcription downstream of genes (DoG). In this study, we performed a detailed comparison of DoTT/DoG transcription between HSV-1 infection, salt and heat stress in primary human fibroblasts using 4sU-seq and ATAC-seq. Although DoTT at late times of HSV-1 infection was substantially more prominent than DoG transcription in salt and heat stress, poly(A) read-through due to DoTT/DoG transcription and affected genes were significantly correlated between all three conditions, in particular at earlier times of infection. We speculate that HSV-1 either directly usurps a cellular stress response or disrupts the transcription termination machinery in other ways but with similar consequences. In contrast to previous reports, we found that inhibition of Ca2+ signaling by BAPTA-AM did not specifically inhibit DoG transcription but globally impaired transcription. Most importantly, HSV-1-induced DoTT, but not stress-induced DoG transcription, was accompanied by a strong increase in open chromatin downstream of the affected poly(A) sites. In its extent and kinetics, downstream open chromatin essentially matched the poly(A) read-through transcription. We show that this does not cause but rather requires DoTT as well as high levels of transcription into the genomic regions downstream of genes. This raises intriguing new questions regarding the role of histone repositioning in the wake of RNA Polymerase II passage downstream of impaired poly(A) site recognition.