Rad23 and Rpn10 play synergistic roles in the recognition of ubiquitinated proteins by the proteasome, and loss of both proteins causes growth and proteolytic defects. However, the physiological targets of Rad23 and Rpn10 have not been well defined. We report that rad23Delta rpn10Delta is unable to grow in the presence of translation inhibitors, and this sensitivity was suppressed by translation elongation factor 1A (eEF1A). This discovery suggested that Rad23 and Rpn10 perform a role in translation quality control. Certain inhibitors increase translation errors during protein synthesis and cause the release of truncated polypeptide chains. This effect can also be mimicked by ATP depletion. We determined that eEF1A interacted with ubiquitinated proteins and the proteasome following ATP depletion. eEF1A interacted with the proteasome subunit Rpt1, and the turnover of nascent damaged proteins was deficient in rpt1. An eEF1A mutant (eEF1A(D156N)) that conferred hyperresistance to translation inhibitors was much more effective at eliminating damaged proteins and was detected in proteasomes in untreated cells. We propose that eEF1A is well suited to detect and promote degradation of damaged proteins because of its central role in translation elongation. Our findings provide a mechanistic foundation for defining how cellular proteins are degraded cotranslationally.