The proteasome controls levels of most cellular proteins, and its activity is regulated under stress, quiescence, and inflammation. However, factors determining the proteasomal degradation rate remain poorly understood. Proteasome substrates are conjugated with small proteins (tags) like ubiquitin and Fat10 to target them to the proteasome. It is unclear if the structural plasticity of proteasome-targeting tags can influence substrate degradation. Fat10 is upregulated during inflammation, and its substrates undergo rapid proteasomal degradation. We report that the degradation rate of Fat10 substrates critically depends on the structural plasticity of Fat10. While the ubiquitin tag is recycled at the proteasome, Fat10 is degraded with the substrate. Our results suggest significantly lower thermodynamic stability and faster mechanical unfolding in Fat10 compared to ubiquitin. Long-range salt bridges are absent in the Fat10 structure, creating a plastic protein with partially unstructured regions suitable for proteasome engagement. Fat10 plasticity destabilizes substrates significantly and creates partially unstructured regions in the substrate to enhance degradation. NMR-relaxation-derived order parameters and temperature dependence of chemical shifts identify the Fat10-induced partially unstructured regions in the substrate, which correlated excellently to Fat10-substrate contacts, suggesting that the tag-substrate collision destabilizes the substrate. These results highlight a strong dependence of proteasomal degradation on the structural plasticity and thermodynamic properties of the proteasome-targeting tags.