This article also answers:

• Is it possible to offer a trial period when reactivating a cancelled subscription?

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Yes, this is certainly possible. 

Just hit the Reactivate Subscription option (on the right panel) on the subscription details page and use the Reactivate From field to set the past date (ideally from the previous billing date). This will immediately move the subscription to ACTIVE. 

Here's a screenshot.

 

Furthermore, you can move the subscription to the trial state by giving the trial end date in Trial Ends At field. When this is given, the Reactivate From date acts as the trial start date and the subscription moves to ACTIVE state once the trial ends.

For subscriptions that were cancelled due to Dunning and are being reactivated before the next billing date (at the time of cancellation) will be considered as interm-reactivation, and will not generate a new invoice.

Subscriptions that were cancelled by any other means (UI, API, Customer portal) will end the term immediately and reactivating them will charge the customer for the full term (a new invoice will be generated).

More information on this is here.