I have an older Ruud heat pump. There is a wire going into it that looks like a phone-type cable, but it is broken and as far as I know has been for quite a while. What would this line do? The heat pump is old and noisy but works as expected and doesn’t use an unreasonable amount of electricity.
Many years ago the power company here offered a rate discount if they could use a device to turn the A/C off for a few moments.
At work, the vendor has a modem on A/C devices so they can monitor their condition.
Wouldn’t that involve more than just one wire going into the heat pump?
If it is phone like, it may have carried some signal between the heat pump and some external device.
It may have been a temperature sensor somewhere outside.
I’m hoping someone that knows more than I will show up. 
Take a photograph and post it here if you want a more certain answer.
You really should take a photograph of the plate on the side showing the model number. That would allow us to look up the electrical diagram for the heat pump.