Cells respond to stress in the ER by initiating the widely conserved unfolded protein response. Activation of the ER transmembrane nuclease IRE1 leads to the degradation of specific mRNAs, but how this pathway affects the ability of cells to recover from stress is not known. Here, we show that degradation of the mRNA encoding biogenesis of lysosome-related organelles 1 subunit 1 (Blos1) leads to the repositioning of late endosomes (LEs)/lysosomes to the microtubule-organizing center in response to stress in mouse cells. Overriding Blos1 degradation led to ER stress sensitivity and the accumulation of ubiquitinated protein aggregates, whose efficient degradation required their independent trafficking to the cell center and the LE-associated endosomal sorting complexes required for transport. We propose that Blos1 regulation by IRE1 promotes LE-mediated microautophagy of protein aggregates and protects cells from their cytotoxic effects.