The 26S proteasome (26SP) is a multi-subunit, multi-catalytic protease that is responsible for most of the cytosolic and nuclear protein turnover. The 26SP is composed of two sub-particles, the 19S regulatory particle (RP) that binds and unfolds protein targets, and the 20S core particle (20SP) that degrades proteins into small peptides. Most 26SP targets are conjugated to a poly-ubiquitin (Ub) chain that serves as a degradation signal. However, some targets, such as oxidized proteins, do not require a poly-Ub tag for proteasomal degradation, and recent studies have shown that the main protease in this Ub-independent pathway is free 20SP. It is currently unknown how the ratio of 26SP- to 20SP-dependent proteolysis is controlled. Here we show that loss of function of the Arabidopsis RP subunits RPT2a, RPN10 and RPN12a leads to decreased 26SP accumulation, resulting in reduced rates of Ub-dependent proteolysis. In contrast, all three RP mutants have increased 20SP levels and thus enhanced Ub-independent protein degradation. As a consequence of this shift in proteolytic activity, mutant seedlings are hypersensitive to stresses that cause protein misfolding, and have increased tolerance to treatments that promote protein oxidation. Taken together, the data show that plant cells increase 20SP-dependent proteolysis when 26SP activity is impaired.