My iMac it’s stuck on an OS X update, frozen and will not restart or reboot

Restart in the Recovery Partition (hold down Command + R on startup) and open Disk Utility and run First Aide on the internal drive several times. If ANY errors appear then your internal drive is damaged and needs to be replaced, no it was not done by Mac OS it was likely a failing drive and the update pushed it over the edge. This is rare but it does happen with major updates.

If no errors appear in Disk Utility, then exit DU and reinstall Mac OS, this will not overwrite your data but will fill in damaged portions of Mac OS. Then restart normally and test.

Finally what year is this iMac???

How long has it been stuck?

Force quit it by holding down the power button. Then attempt to restart by doing a normal restart to check and see if your update completed.