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This simplifies teardown, especially in ash on Chrome OS.

Also add tests for the code in crrev.com/c/1180070 which generally
skips event dispatch during shutdown.

Bug: 874156
Test: added to aura_unittests
Change-Id: I1356c3a1ab09f07d23dca1545d3159fcc4016e2d
Reviewed-on: https://chromium-review.googlesource.com/1181537Reviewed-by: Sadrul Chowdhury <sadrul@chromium.org>
Commit-Queue: James Cook <jamescook@chromium.org>
Cr-Commit-Position: refs/heads/master@{#585324}