How to go about it will depend on what's available.
For example, if the PLC already knows the line speed, then by adding a sensor that signals once per revolution of the unwind, you can calculate the unwind diameter by keeping track of the time per revolution. Knowing the diameter of the roll, you can automatically stop when reaches a minimum diameter. Of course, if you use different size cores, you will have to provide some way to compensate.
If your PLC doesn't know the line speed, you can mount a photocell that looks across the unwind and is blocked by the roll. When the roll winds down and the photocell gets cleared, you can either stop immediately or warn the operators to slow down and prepare to stop. In that case, if you use different size cores, you will have to adjust the position of the photocell when you change the chucks.
There are also ultrasonic or laser sensors that can measure the roll diameter.