Yes. The endoplasmic reticulum can stop working.

The endoplasmic reticulum (ER) performs a number of functions including protein synthesis, folding, and sorting, calcium homeostasis, and lipid biosynthesis. The proper functioning of the ER can be disrupted by several different physiological and pathological conditions. This disruption in the functioning of the ER causes ER stress, which impairs the protein folding process.

Accumulation of excessive misfolded or unfolded proteins causes the endoplasmic reticulum to malfunction or stop altogether posing a proteotoxic threat to the survival of the cell.