When nutrients in their environment are exhausted, bacterial cells become arrested for growth. During these periods, a primary challenge is maintaining cellular integrity with a reduced capacity for renewal or repair. Here, we show that the heat-shock protease FtsH is generally required for growth arrest survival of Pseudomonas aeruginosa, and that this requirement is independent of a role in regulating lipopolysaccharide synthesis, as has been suggested for Escherichia coli We find that ftsH interacts with diverse genes during growth and overlaps functionally with the other heat-shock protease-encoding genes hslVU, lon, and clpXP to promote survival during growth arrest. Systematic deletion of the heat-shock protease-encoding genes reveals that the proteases function hierarchically during growth arrest, with FtsH and ClpXP having primary, nonredundant roles, and HslVU and Lon deploying a secondary response to aging stress. This hierarchy is partially conserved during growth at high temperature and alkaline pH, suggesting that heat, pH, and growth arrest effectively impose a similar type of proteostatic stress at the cellular level. In support of this inference, heat and growth arrest act synergistically to kill cells, and protein aggregation appears to occur more rapidly in protease mutants during growth arrest and correlates with the onset of cell death. Our findings suggest that protein aggregation is a major driver of aging and cell death during growth arrest, and that coordinated activity of the heat-shock response is required to ensure ongoing protein quality control in the absence of growth.