This process is again tied up to the procedures of the respective FNO. In most cases, the previous tenant/owner gives notice of cancellation, and at the end of the cancellation period the line is marked as "freed by the ISP".
This allows the new owner/tenant to access and signup for the line through the ISP of their choice.
The ISP is always responsible for paying the line fee, so it doesn't make sense that someone else just "takes" it over, unless you basically hand them the account and tell them to update their details, but even then it's a risky move, as you would have originally been RICA'd on the account using your details.
It's better to just cancel the service, and let the new owner deal with the ISP of their choice.