Correct. The control pilot signal from EVSE to EV is a PWM signal that indicates to the EV how much current is available.
It could drop at any time due to, for example, many chargers being connected to 1 circuit and the chargers coordinating with each-other to load-balance their connected vehicles (everyone gets their fair share), or it could be tied to solar PV generation so that charging doesn't import from the grid; the available current will change with how much excess PV is available, etc.
A well-engineered EVSE will notice when the EV is drawing more than the EVSE wants it to. It should then open the mains contactor at this point; cutting the EV's electricity supply. It will also hold the control pilot low to signal a fault to the EV.