For some time, it has been possible, using mathematical models, to compute whether an isotope of an element should be stable, or subject to decay. This is one of the advances in science since I left high school.
As a result, in recent years, it has been discovered that two isotopes formerly throught to be stable are in fact unstable. However, they have such enormously long half-lives that until recently it was not even possible to detect decay in samples of those isotopes, since it would take a significant period of time to detect even a single decay event, and measurement technology was unable to detect such an event given all of the other background radiation and events that normally occur in nature.
Thanks to advances in technology, we know now that Bismuth-209 and Tellurium-128 are in fact not stable isotopes. However, for all practical purposes they are. The half-life of Bismuth-208 is 1.9×10¹⁹ years, and the half-life of Tellurium-128 is an even more mind-boggling 2.2×10²⁴ years.
As this article makes clear, it is possible that further technology advances will make it possible for us to observe radioactive decay in some isotopes previously classed as stable. However, a large number of isotopes, using existing predictive models, do not have any possible decay modes.