You have the option to automatically handle situations when customers have overdue invoices: In a certain time, Business Manager starts sending such customers notifications that remind about overdue invoices. If the customers do not close the invoices, the system suspends their unpaid subscriptions. However, you can restrict suspending subscriptions of certain customers as described in the section Limiting Discounts and Exempting Subscriptions from Suspension.
Also, Business Manager checks automatically suspended subscriptions with a periodic task to see if the associated invoice has been paid. If it has been paid, the system will activate the subscription.
The settings that define how to handle unpaid subscriptions are available at the Business Setup > All Settings > Cancelation of Unpaid Subscriptions page.