Cells have quality-control mechanisms to recognize non-native protein structures and either help the proteins fold or promote their degradation. Ubiquitin-conjugating enzymes (E2s) and ubiquitin ligases (E3s) work together to assemble polyubiquitin chains on misfolded or misassembled proteins, which are then degraded by the proteasome. Here, we find that Ubc7, a yeast E2, can itself undergo degradation when its levels exceed that of its binding partner Cue1, a transmembrane protein that tethers Ubc7 to the endoplasmic reticulum. Unassembled, and thus mislocalized, Ubc7 is targeted to the proteasome by Ufd4, a homologous to E6-AP C-terminus (HECT)-class E3. Ubc7 is autoubiquitinated by a novel mechanism wherein the catalytic cysteine, instead of a lysine residue, provides the polyubiquitin chain acceptor site, and this cysteine-linked chain functions as a degradation signal. The polyubiquitin chain can also be transferred to a lysine side chain, suggesting a mechanism for polyubiquitin chain assembly that precedes substrate modification.