Cardiomyopathies, neuropathies, cancer and accelerated ageing are unequivocally distinct diseases, yet they also show overlapping pathological hallmarks, including a gradual loss of genomic integrity and proteotoxic stress. Recent lines of evidence suggest that this overlap could be the result of remarkably interconnected molecular cascades between nuclear genomic instability and a loss of protein homeostasis. In this review, we discuss these complex connections, as well as their possible impact on disease. We focus in particular on the inherent ability of a wide range of genomic alterations to challenge protein homeostasis. In doing so, we provide evidence suggesting that a loss of protein homeostasis could be a far more prevalent consequence of genomic instability than generally believed. In certain cases, such as aneuploidy, a loss of protein homeostasis appears to be a crucial mechanism for pathology, which indicates that enhancing protein quality control systems could be a promising therapeutic strategy in diseases associated with genomic instability.