Yes, this would be "suspend". Clients can cancel by logging into the member's area and clicking to cancel. If you won't be using the member’s area, then you'd need to submit an incoming API call for that. The mode would be "unsubscribe" for the incoming API. You’d need to store the client's Nanacast ID when you get the original outgoing API notification so that you can submit it to Nanacast via the incoming API should they ever cancel. 

You can go to Advanced >> Outgoing API for more details.

Keywords: Outgoing API