Specifically with Stripe (check with your payment processor on this), when the retry process wraps up a customer can either be marked as unpaid, or canceled.
Whenever a card is updated, you can decide how far back you’d like to go for collecting unpaid invoices. But only if your Stripe settings are set to leave a customer's subscription as "unpaid". Not "canceled".
Beyond re-activating the subscription, you can also collect for any invoices that went unpaid in that time frame.
Some companies like to collect all unpaid invoices, others only go back 30–60 days. And some prefer to just forgive the balance and move on.
The specifics depend on your business model, so make sure you put thought into this and get set up with the proper custom solution.
Make sure you set the right expectations - you don’t want customers to be surprised when they get charged $100 18 times when they update their card after an extended-delinquency.