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Now, the way I would implement your use case is as follows:
I would make a plan that has a different first period duration and cost and follow-up period would be your regular one month duration and regular one month price.
I would have the first duration set to 2 months at the same one month price.
This way when a user subscribes for the very first time they get 2 months for the price of 1. After end of first 2 month period subscriber will be billed for each additional month at regular price.
please specify what exactly do you mean by "when a member quits"?
if you have properly configured your plan and gateway (you haven't stated yours) and they both support recurring payments, then your subscriber will be automatically billed/debited each month until they specifically end their subscription from their profile. If something goes bad and payment is not received, then CBSubs of course will block any privileges associated with the plan in question.
BTW - if you have not already done so, please read the CBSubs documentation.