This is Summer from the Social Care team at Shopify. Welcome to Shopify Community!
Domains have an auto-renew setting to ensure that your domain ownership doesn't expire and to avoid any store downtime caused by domain expirations. If you have a Shopify domain, this setting can be toggled on or off within the Online Store > Domains page in your admin. If auto-renew has been left enabled when you closed your store, the domain will continue to renew and will incur an annual registration fee. To stop the domain registration from renewing, auto-renew needs to be turned off. I outlined the steps to disable auto-renew below, after the discussion on how to access your store while it's closed.
If your account does not have outstanding invoices and you closed your store by following the steps on this page, we can look into providing temporary admin access for you to disable auto-renew on Shopify domains. Our support team can check your account and see if this is an option. You may contact them through this page.
If your account has an outstanding invoice, this needs to be settled in order to gain access to the admin. You will be prompted to settle the outstanding invoice when you log in to your Shopify admin. Once this is settled, you can reactivate the store and choose a plan to gain access to the admin. If you don't have any plans of continuing with the store, you may immediately close it after disabling auto-renew. We don't provide refunds as per our Terms of Service but we can look into possibly providing a refund in this situation. To inquire about a possible refund, you may also contact our support team through this page.
When you're logged in to your Shopify admin, you may simply follow the steps below to disable auto-renew on your Shopify domain.
If you have a third-party domain, the domain provider may have a different procedure in canceling the domain. For advice and assistance on the exact steps, you can contact the third-party domain provider's support team.
Please note that canceling your domain will release it from your ownership and the domain will become available to be purchased and registered by somebody else. If you want to keep it and plan to use it on another platform, you can transfer your domain to a different domain provider. This can be done when it's been more than 60 days since you purchased your domain. If you reactivate your Shopify store in the future and you've transferred your domain, you can still use it and connect it to the store.
Is there any particular reason why you closed your store and wanted to let go of the domain?