Q:

what about the docker image if a container is crashed?

For my opinion, a container is a running instance of image. What if the container is crashed, for example run sudo rm -f / delete all the stuffs, is the docker image still OK?

A:

No effect for image in both cases.
Look if you create new container via docker run, virtually new layer

When you create a new container, you add a new, thin, writable layer on top of the underlying stack. This layer is often called the “container layer”. All changes made to the running container - such as writing new files, modifying existing files, and deleting files - are written to this thin writable container layer. The diagram below shows a container based on the Ubuntu 15.04 image.
  src

This stackopverflow discussion may be helpful as well:
Docker image vs container

