As soon as a membership goes into arrears it cannot be used as a payment method. The arrears must be cleared for it to be used again. Any other configured payment method options such as, for example, pay-as-you-go via card, would, however, still be available to the customer.
On the next billing date, if the Membership is still In Arrears then the membership will be marked as Failed. This causes the following:
A notification will be sent to the customer informing them of the cancelled membership.
All future event bookings made using the membership will be cancelled with no refund being processed.
No future bookings can be made using the membership.
As the membership is failed due to arrears, the customer will not be able to purchase a new instance of the Membership.