A Customer should only be removed from a Subscription if they receive a Refund or you had to take another form of payment for their balance.
To Remove a Customer from a Subscription in Stripe:
Log in
Find Customer - Type name in Search Window
Select the Customer
Under Subscriptions click ... to expand and click Cancel Subscription
Choose Immediately
Click End Subscription
When a Customer is removed from a Subscription all future invoices and payment attempts will be stopped. If there are already unpaid Invoices they will need to be "Forgiven" so the customer does not show up as delinquent.
Remove Customer from Delinquent List