Application Shutdown only works when running in ANCM-inproc

Deploy a V2 app with the latest bits (using private site extension) and then drop in the APP_OFFLINE.htm file and the app crashes and goes into a bad state.

Start by reproducing the reported behavior with a V2 app using the latest private site extension bits, then deploy it under ANCM-inproc and drop in APP_OFFLINE.htm. Compare the shutdown behavior and identify what leads to the crash or bad state. Done means application shutdown works without either failure mode.

Written by the indexing model from the issue text.