Flaviviruses such as Yellow fever, Dengue, West Nile, and Zika generate disease-linked viral noncoding RNAs called subgenomic flavivirus RNAs. Subgenomic flavivirus RNAs result when the 5′–3′ progression of cellular exoribonuclease Xrn1 is blocked by RNA elements called Xrn1-resistant RNAs located within the viral genome’s 3′-untranslated region that operate without protein co-factors. Here, we show that Xrn1-resistant RNAs can halt diverse exoribonucleases, revealing a mechanism in which they act as general mechanical blocks that ‘brace’ against an enzyme’s surface, presenting an unfolding problem that confounds further enzyme progression. Further, we directly demonstrate that Xrn1-resistant RNAs exist in a diverse set of flaviviruses, including some specific to insects or with no known arthropod vector. These Xrn1-resistant RNAs comprise two secondary structural classes that mirror previously reported phylogenic analysis. Our discoveries have implications for the evolution of exoribonuclease resistance, the use of Xrn1-resistant RNAs in synthetic biology, and the development of new therapies.