Log out stuck because of Dock

We have two 2.8 i7 Mid-2011 iMacs running 10.11.6. They've started acting very odd. User accounts are set up locally on the machine. Users can log in and use the Mac as normal but when they log out it seems as if a process is still continuing. Their Dock remains at the bottom of the screen and their account is still active (as visible from ARD). Commands to shut down, restart etc. don't work and the only way to exit is to manually reset via the power button.

Any ideas on why this is happening and how to pinpoint the process causing issues?