ISG20 is an IFN-induced 3′–5′ RNA exonuclease that acts as a broad antiviral factor. At present, the features that expose RNA to ISG20 remain unclear, although recent studies have pointed to the modulatory role of epitranscriptomic modifications in the susceptibility of target RNAs to ISG20. These findings raise the question as to how cellular RNAs, on which these modifications are abundant, cope with ISG20. To obtain an unbiased perspective on this topic, we used RNA-seq and biochemical assays to identify elements that regulate the behavior of RNAs against ISG20. RNA-seq analyses not only indicate a general preservation of the cell transcriptome, but they also highlight a small, but detectable, decrease in the levels of histone mRNAs. Contrarily to all other cellular ones, histone mRNAs are non-polyadenylated and possess a short stem–loop at their 3′ end, prompting us to examine the relationship between these features and ISG20 degradation. The results we have obtained indicate that poly(A)-binding protein loading on the RNA 3′ tail provides a primal protection against ISG20, easily explaining the overall protection of cellular mRNAs observed by RNA-seq. Terminal stem–loop RNA structures have been associated with ISG20 protection before. Here, we re-examined this question and found that the balance between resistance and susceptibility to ISG20 depends on their thermodynamic stability. These results shed new light on the complex interplay that regulates the susceptibility of different classes of viruses against ISG20.