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Because we don't know when the app will be killed, the current
time before Directory saves can result in lost data. This
change uses the app getting backgrounded as a signal that we
might be killed soon and triggers a Directory::SaveChanges().

BUG=395233

Review URL: https://codereview.chromium.org/551843003

Cr-Commit-Position: refs/heads/master@{#297547}