Okay I think I understand now: I can't serve custom error pages because the whole app pool is broken. So .NET nor IIS as a web server can't do anything - no redirect, no execute url, no file content serving, nothing.... It's because the app pool itself isn't working. To make custom error pages work the application pool must be running. In my case the app pool is not running because during the initialization of the app pool there is the exception leading to a broken/not running app pool.

The only way how to do it when I think about it right now is to use a reverse proxy server where I can set custom error pages. Then in this case when a backend isn't working I can serve custom error page from my reverse proxy server.
Or I can use more resilient solution where I will implement a load balancer.