Although RNA polymerase II (Pol II) productively transcribes very long genes in vivo, transcription through extragenic sequences often terminates in the promoter-proximal region and the nascent RNA is degraded. Mechanisms that induce early termination and RNA degradation are not well understood in multicellular organisms. Here, we present evidence that the suppressor of sable su(s) regulatory pathway of Drosophila melanogaster plays a role in this process. We previously showed that Su(s) promotes exosome-mediated degradation of transcripts from endogenous repeated elements at an Hsp70 locus (Hsp70-αβ elements). In this report, we identify Wdr82 as a component of this process and show that it works with Su(s) to inhibit Pol II elongation through Hsp70-αβ elements. Furthermore, we show that the unstable transcripts produced during this process are polyadenylated at heterogeneous sites that lack canonical polyadenylation signals. We define two distinct regions that mediate this regulation. These results indicate that the Su(s) pathway promotes RNA degradation and transcription termination through a novel mechanism.