All they will do is send you a letter saying that they are no longer offering the service to you...you will likely see one of two approaches:
- A full refund for your "last month of service"
- A pro-rated refund for the remainder of your paid service (monthly in most cases)
It is entirely up to the company to decide who they want to do business with.
The problem is going to come if a company offers more than one service to a customer. In the case of a cable company, how likely is a customer that has had their internet access cut off going to be to keep their cable tv service?
I personally pay ~$40 for cable internet service, but my monthly cable bill is ~$120. I can guarantee you that if the cable company cuts off my cable internet, they will lose the whole $120 from me.