Fix shutdown crash in ProfileManager.

OnProfileMarkedForPermanentDeletion should move from
ProfileManagerObserver to ProfileObserver, which would also
fix this bug. However, changing the order of members is the
quickest and most cherry-pick-able way to avoid the crash.

Bug: 1005244
Change-Id: If2db68c846dd418cd02864b57b9b543687fa1e03
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1863518
Auto-Submit: Evan Stade <estade@chromium.org>
Reviewed-by: David Roger <droger@chromium.org>
Commit-Queue: Evan Stade <estade@chromium.org>
Cr-Commit-Position: refs/heads/master@{#706467}

chrome/browser/profiles/profile_manager.h

@@ -410,6 +410,10 @@ class ProfileManager : public content::NotificationObserver,
       const base::FilePath& profile_dir);
 #endif  // !defined(OS_ANDROID)
 
+  // Destroy after |profile_info_cache_| since Profile destruction may trigger
+  // some observers to unregister themselves.
+  base::ObserverList<ProfileManagerObserver> observers_;
+
   // Object to cache various information about profiles. Contains information
   // about every profile which has been created for this instance of Chrome,
   // if it has not been explicitly deleted. It must be destroyed after
@@ -451,8 +455,6 @@ class ProfileManager : public content::NotificationObserver,
   // Controls whether to initialize some services. Only disabled for testing.
   bool do_final_services_init_ = true;
 
-  base::ObserverList<ProfileManagerObserver> observers_;
-
   // TODO(chrome/browser/profiles/OWNERS): Usage of this in profile_manager.cc
   // should likely be turned into DCHECK_CURRENTLY_ON(BrowserThread::UI) for
   // consistency with surrounding code in the same file but that wasn't trivial