This is usually caused by the external usb drive not being available for an overnight backup (why is another issue). The system drive’s mount point for the USB: /external then get’s filled up with what should have gone to the USB. Diagnose using df from a TTY prompt at the hung screen.
/dev/sdb2 will show 100% full and 0 space available on it
IMPORTANT don’t run the commands below with the USB drive connected, if it has re-mounted the backup will be deleted. For safety boot into temp system from a pendrive
You can access a tty shell by pressing CTRL+AL+F1 if the gui login keeps coming back, or if the login doesn’t get to that stage.
sudo rm -rf /external/home will delete the appropriate subfolders on the system mount point. check df again.
CTRL+AL+F7 should get you back to the gui loging screen
IF you have trouble with the deleted files being moved to trash and still not releasing drive space, also:
sudo rm -rf /external/home/.Trash-1000
releases the space
Remedial work: find a way of not making this happen then the USB drive ‘dissapears’?