Under both simple random sampling and stratified random sampling from a study region, we develop a Bayesian, asymptotic lower limit for the expected number of the region's classes that are not observed in the sample. In practical applications, the classes might be species in a forest or types of defects in a product line. The aforementioned lower limit is extremely robust to the prior on θ, the total number of classes in the region. We also consider a potential lower limit for θ. Both the lower limit on the expected number of unobserved classes and the lower limit on θ were conservative in our simulations.