When using Stripe to collect recurring/subscription payments, Stripe have a 'Smart Retry' feature available where it will retry up to four times over a period of time. These 4 attempts can be set over 1 week, 2 weeks, 3 weeks or 1 month. You can manage these settings from within your Stripe account. If the fourth attempt of collecting the payment fails the subscription will either stay as it is, change to 'unpaid', or change to 'cancelled'. Again you can manage this setting from within your stripe account also. The status may be set to 'cancel the subscription' by default.
There are no fees charged for failed payments.
Alternatively rather then using the 'Smart Retry' service, you can use 'Custom Retry Schedule' which will allow you to create your own rules for failed payements.
To view/manage your settings login to your Stripe account. Click on the 'Settings' menu. Then click on the 'Subscriptions and emails' setting.
Custom Retry Schedule
When you update your settings, remember to 'Save' them.