Assemblysomes are EDTA- and RNase-resistant ribonucleoprotein (RNP) complexes of paused ribosomes with protruding nascent polypeptide chains. They have been described in yeast and human cells for the proteasome subunit Rpt1, and the disordered amino-terminal part of the nascent chain was found to be indispensable for the accumulation of the Rpt1-RNP into assemblysomes. Motivated by this, to find other assemblysome-associated RNPs we used bioinformatics to rank subunits of Saccharomyces cerevisiae protein complexes according to their amino-terminal disorder propensity. The results revealed that gene products involved in DNA repair are enriched among the top candidates. The Sgs1 DNA helicase was chosen for experimental validation. We found that indeed nascent chains of Sgs1 form EDTA-resistant RNP condensates, assemblysomes by definition. Moreover, upon exposure to UV, SGS1 mRNA shifted from assemblysomes to polysomes, suggesting that external stimuli are regulators of assemblysome dynamics. We extended our studies to human cell lines. The BLM helicase, ortholog of yeast Sgs1, was identified upon sequencing assemblysome-associated RNAs from the MCF7 human breast cancer cell line, and mRNAs encoding DNA repair proteins were overall enriched. Using the radiation-resistant A549 cell line, we observed by transmission electron microscopy that 1,6-hexanediol, an agent known to disrupt phase-separated condensates, depletes ring ribosome structures compatible with assemblysomes from the cytoplasm of cells and makes the cells more sensitive to X-ray treatment. Taken together, these findings suggest that assemblysomes may be a component of the DNA damage response from yeast to human.