How to fix a frozen gnome-shell without restarting X?

If you have access to a Linux virtual terminal (Ctrl + Alt + F1 and so on), you can solve this issue without restarting the X Window System:

1. Go to a virtual terminal and log in.
2. Execute:
   gnome-shell --replace --display=:0.0 &
3. You may now log out again (press Ctrl + D). The new gnome-shell will not be affected, as it runs in the background.