The ubiquitin receptors Rad23 and Dsk2 deliver polyubiquitylated substrates to the proteasome for destruction. The C-terminal ubiquitin-associated (UBA) domain of Rad23 functions as a cis-acting stabilization signal that protects this protein from proteasomal degradation. Here, we provide evidence that the C-terminal UBA domains guard ubiquitin receptors from destruction by preventing initiation of degradation at the proteasome. We show that introduction of unstructured polypeptides that are sufficiently long to function as initiation sites for degradation abrogates the protective effect of UBA domains. Vice versa, degradation of substrates that contain an unstructured extension can be attenuated by the introduction of C-terminal UBA domains. Our study gains insight into the molecular mechanism responsible for the protective effect of UBA domains and explains how ubiquitin receptors can shuttle substrates to the proteasome without themselves becoming subject to proteasomal degradation.