The accumulation of toxic protein aggregates is thought to play a key role in a range of degenerative pathologies, but it remains unclear why aggregation of polypeptides into non-native assemblies is toxic and why cellular clearance pathways offer ineffective protection. We here study the A4V mutant of SOD1, which forms toxic aggregates in motor neurons of patients with familial amyotrophic lateral sclerosis (ALS). A comparison of the location of aggregation prone regions (APRs) and Hsp70 binding sites in the denatured state of SOD1 reveals that ALS-associated mutations promote exposure of the APRs more than the strongest Hsc/Hsp70 binding site that we could detect. Mutations designed to increase the exposure of this Hsp70 interaction site in the denatured state promote aggregation but also display an increased interaction with Hsp70 chaperones. Depending on the cell type, in vitro this resulted in cellular inclusion body formation or increased clearance, accompanied with a suppression of cytotoxicity. The latter was also observed in a zebrafish model in vivo. Our results suggest that the uncontrolled accumulation of toxic SOD1A4V aggregates results from insufficient detection by the cellular surveillance network.