Avoid exception when an exception is thrown in Request handling

BUG=337870
NOTRY=true

Review URL: https://codereview.chromium.org/146613004

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@246942 0039d316-1c4b-4281-b951-d872f2087c98
SVN changes up to revision 246942