Therapy resistance in cancer is often driven by a subpopulation of cells that are temporarily arrested in a non-proliferative, quiescent or ‘dormant’ state, which is difficult to capture and whose mutational drivers remain largely unknown. We developed methodology to uniquely identify this state from transcriptomic signals and characterised its prevalence and genomic constraints in solid primary tumours. We show dormancy preferentially emerges in the context of more stable, less mutated genomes which maintain TP53 integrity and lack the hallmarks of DNA damage repair deficiency, while presenting increased APOBEC mutagenesis. We uncover novel genomic dependencies of this process, including the amplification of the centrosomal gene CEP89 as a driver of dormancy impairment. Lastly, we demonstrate that dormancy underlies unfavourable responses to various therapies exploiting cell cycle, kinase signalling and epigenetic mechanisms in single cell data, and propose a signature of dormancy-linked therapeutic resistance to further study and clinically track this state.