How to prevent floating input for this system?
A simple pull-down resistor (connection to GND via resitor) at the input can fix the problem. 

It would pull down the floating potential of the open line to 0V. 

Note: This works if the output impedance of the "voltage input" part (A) is low enough.
It wouldn't be good if the "input voltage" part (A) is just a potentiometer because then the pull down resistor would influence the control voltage.