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Make it use DeleteDelegate() to be more consistent with
StatusAreaWidgetDelegate. Defer closing the widget until all the
top-level windows are closed. Don't try to close all windows more than
once during shutdown, which simplifies the shelf cleanup code.

Originally landed as cc4be1cb.

That version exposed a use-after-free in ash drag and drop code,
which was fixed separately. See https://crbug.com/818603

TBR=sadrul@chromium.org

Bug: 628655, 818603
Test: ash_unittests
Change-Id: I4a8ade351456b476a19225f2c740e031f6b0e122
Reviewed-on: https://chromium-review.googlesource.com/956924
Commit-Queue: James Cook <jamescook@chromium.org>
Reviewed-by: Michael Wasserman <msw@chromium.org>
Cr-Commit-Position: refs/heads/master@{#542308}