The role of cytosolic stress granules in the integrated stress response has remained largely enigmatic. Here, we studied the functionality of the ubiquitin-proteasome system (UPS) in cells that were unable to form stress granules. Surprisingly, the inability of cells to form cytosolic stress granules had primarily a negative impact on the functionality of the nuclear UPS. While defective ribosome products (DRiPs) accumulated at stress granules in thermally stressed control cells, they localized to nucleoli in stress granule-deficient cells. The nuclear localization of DRiPs was accompanied by redistribution and enhanced degradation of SUMOylated proteins. Depletion of the SUMO-targeted ubiquitin ligase RNF4, which targets SUMOylated misfolded proteins for proteasomal degradation, largely restored the functionality of the UPS in the nuclear compartment in stress granule-deficient cells. Stress granule-deficient cells showed an increase in the formation of mutant ataxin-1 nuclear inclusions when exposed to thermal stress. Our data reveal that stress granules play an important role in the sequestration of cytosolic misfolded proteins, thereby preventing these proteins from accumulating in the nucleus, where they would otherwise infringe nuclear proteostasis.