OS volume shows as type 'FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFF' after attempting to delete some Linux partitions—cannot log in
To correct the GUID error in your GPT, you need to start up from OS X Recovery over the Internet or from a USB drive with the macOS Installer flashed on it. To boot into recovery mode press and hold the command(⌘)optionR keys immediately after you turn on your Mac and hear the startup sound. To boot into a USB key, hold option immidiatly after you turn on your Mac. You will be prompted to select a drive, one of which will be titled something similar ot "macOS Installer" which you will need to select. For more information see the site: OS X: About OS X Recovery. Once started to OS X Recovery or the Installer, select the Terminal application from the menu bar. Enter the following commands to repair your GPT.

diskutil  unmountdisk  /dev/disk0
gpt  remove  -i  2  /dev/disk0
diskutil  unmountdisk  /dev/disk0
gpt  add  -i  2  -b  409640  -s  194016208  -t  hfs  /dev/disk0



  Note: I do not know if this will fix your log in problems.