LinuxCNC and Mesa can do closed loop everything, even dual feedback closed loop (i.e. incremental encoders on motor shaft and linear scales for the same axis), but from your post it is not clear if you mean using closed loop stepper/drive AND closed loop in LinuxCNC = still works on LinuxCNC, or stepper/drives with no feedback and encoders closed in LinuxCNC = also works in LinuxCNC.
The only issue is when using closed loop stepper/drives and using the same encoders for LinuxCNC feedback ( even this will work for sure ) but might need some signal shaping and/or splitting to have the same encoder wired to two inputs on the drive and Mesa board.
BTW, LinuxCNC can do all this with a simple parallel port, although with very limited speed.
EDIT:
Closed loop stepper/drives have a fault output that can be used to stop the machine when the drive detects it's lost position.