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These tests previously relied upon QuitCurrent*Deprecated() to terminate
RunLoops when the expected conditions arose.

Bug: 844016
Change-Id: I290599b94936b2ef253925f6f58b67d017b4603b
Reviewed-on: https://chromium-review.googlesource.com/1107242Reviewed-by: Alexander Alekseev <alemate@chromium.org>
Reviewed-by: Maksim Ivanov <emaxx@chromium.org>
Commit-Queue: Wez <wez@chromium.org>
Cr-Commit-Position: refs/heads/master@{#569563}