If my rack loses a phase of power, especially a phase that does not serve power to the UI/processor, how will the 0-10v lines on that phase react? Will they be forced open or remain the same as before?
The 0-10v circuits will remain the same as before, and not forced open. As these racks do not have an internal sense feed to detect phase loss, their processor does not have the capability to react based on phase loss. However, the 0-10v lines are forced open if the processor loses power, so if the phase that powers the processor goes down, you will see this happen.
If you want your rack to enter an emergency/panic state upon phase loss, you will need to tie the rack's panic input to an EBDK or equivalent, which can sense phase loss and trigger an emergency state.