Just like the Rust executable is still on disk. Sure, if it is running, it is memory mapped, but it can still be paged out. This is not theoretical. In practice, upon request, the probability of finding the static page in cache should be similar to the probability of the executable not being paged out. (That's true as long as the actual data is the same, and the differing factors, like the size of the web server executable, are small compared to the amount of free memory.)
Interesting. I've never heard of that happening before. Can you link a reference to where I can find out more about that aspect of the linux memory subsystem?