This study investigates the mechanism by which stress responses are silenced in cells, focusing on a large E3 ligase complex called SIF1, which is mutated in ataxia and early-onset dementia. SIF1 plays a crucial role in silencing the cellular response to mitochondrial protein import stress by degrading both unimported mitochondrial precursors and stress response components. The study reveals that SIF1 recognizes and ubiquitylates specific motifs in these proteins, which are also used for protein localization and stability. This process involves the recognition of bifunctional motifs that encode both protein localization and stability, referred to as "converging degrons." The study also demonstrates that SIF1 preferentially targets active forms of the stress response kinase HRI and the sensor DELE1, which are involved in the integrated stress response (ISR). Pharmacological restoration of stress response silencing in SIF1 mutant cells can sustain cell survival even when stress resolution fails, highlighting the importance of timely signal termination in maintaining cellular health. The findings provide a roadmap for treating neurodegenerative diseases caused by mitochondrial import defects.This study investigates the mechanism by which stress responses are silenced in cells, focusing on a large E3 ligase complex called SIF1, which is mutated in ataxia and early-onset dementia. SIF1 plays a crucial role in silencing the cellular response to mitochondrial protein import stress by degrading both unimported mitochondrial precursors and stress response components. The study reveals that SIF1 recognizes and ubiquitylates specific motifs in these proteins, which are also used for protein localization and stability. This process involves the recognition of bifunctional motifs that encode both protein localization and stability, referred to as "converging degrons." The study also demonstrates that SIF1 preferentially targets active forms of the stress response kinase HRI and the sensor DELE1, which are involved in the integrated stress response (ISR). Pharmacological restoration of stress response silencing in SIF1 mutant cells can sustain cell survival even when stress resolution fails, highlighting the importance of timely signal termination in maintaining cellular health. The findings provide a roadmap for treating neurodegenerative diseases caused by mitochondrial import defects.