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This patch changes the tests to just wait for tasks to finish before
running their validation instead of relying on the timing of particular
threads. Also fixed a property leak on shutdown that was probably
causing their flakiness, so they are re-enabled.

Bug: 396344, 689520
Change-Id: I9f04d515279ec10f6353e0e6c096ca76bda8ed1c
Reviewed-on: https://chromium-review.googlesource.com/575758Reviewed-by: Scott Violet <sky@chromium.org>
Reviewed-by: Greg Thompson <grt@chromium.org>
Reviewed-by: Peter Kasting <pkasting@chromium.org>
Commit-Queue: Bret Sepulveda <bsep@chromium.org>
Cr-Commit-Position: refs/heads/master@{#491918}