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I suspect I'm going to need some tuning of exit. Unfortunately
chrome shutdown path is pretty hard to observe outside of the code
itself.

BUG=1167296
TEST=SessionServiceLogTest*

Change-Id: Iae2647695be8f6e6932406bbb88df2dd2ab76504
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2641117
Commit-Queue: Scott Violet <sky@chromium.org>
Reviewed-by: David Bienvenu <davidbienvenu@chromium.org>
Cr-Commit-Position: refs/heads/master@{#845789}