For most protein coding genes, termination of transcription by RNA polymerase II is preceded by an endonucleolytic cleavage of the nascent transcript. The 3' product of this cleavage is rapidly degraded via the 5' exoribonuclease Rat1p which is thought to destabilize the RNA polymerase II complex. It is not clear whether RNA cleavage is sufficient to trigger nuclear RNA degradation and transcription termination or whether the fate of the RNA depends on additional elements. For most mRNAs, this cleavage is mediated by the cleavage and polyadenylation machinery, but it can also be mediated by Rnt1p. We show that Rnt1p cleavage of an mRNA is not sufficient to trigger nuclear degradation or transcription termination. Insertion of an Rnt1p target site into a reporter mRNA did not block transcription downstream of the cleavage site, but instead produced two unstable cleavage products, neither of which were stabilized by inactivation of Rat1p. In contrast, the 3' and 5' cleavage products were stabilized by the deletion of the cytoplasmic 5' exoribonuclease (Xrn1p) or by inactivation of the cytoplasmic RNA exosome. These data indicate that transcription termination and nuclear degradation is not the default fate of cleaved RNAs and that specific promoter and/or sequence elements are required to determine the fate of the cleavage products.