[ash-chrome] Do not access UserSessionManager during shutdown

Bug: 1208908
Change-Id: I81a5691b39c4fd0d4c9c653fc581f41c4fb6427c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3009258


Auto-Submit: Roman Sorokin [CET] <rsorokin@chromium.org>
Commit-Queue: Yunke Zhou <yunkez@google.com>
Reviewed-by: Yunke Zhou <yunkez@google.com>
Cr-Commit-Position: refs/heads/master@{#899142}