Absolutely yes.

The risk is highly dependant upon the size of the population, how spread out said population is, if the pathogen is invasive to the population, and the creatures ability to evolve to tolerate said disease ( a factor related to its inherent diversity, life span, number off spring, and reproductive cycle) among others.

Another key consideration is that evolving to over come a pathogen or change in the environment might be enough for off spring (several generations perhaps) to live on but the old species to be classified as extinct.

Extinction and species are just fancy human ideas with limited definition and consistency. For example - neanderthals are considered extinct, but their genetic material remains in humans to this day. Likewise - no species really go extinct ofr just one reason but a multitude of environmental factors.