Hi there,
Thank you for reaching out!
Technically, during the migration/overwrite of the live stage with the staging site, you’ll be performing a subscription migration which is a fairly complicated process and specifics depend on the payment methods you’re using, as well as the plugin you’re using for subscriptions.
You’ll need to export subscriptions from your current live site, import them to the new site, and then disable subscriptions on the old live site so that it doesn’t trigger duplicate subscription renewals.
If you’re using WooCommerce Subscriptions – please note that support of his premium extension is handled on WooCommerce.com, so please open a new ticket from the WooCommerce.com account you used to purchase the license.
More information can be found in these support documents:
https://woocommerce.com/document/migrating-subscribers-woocommerce-subscriptions/
https://woocommerce.com/document/subscriptions/subscriptions-handles-staging-sites/
https://woocommerce.com/document/subscriptions/add-or-modify-a-subscription/
Since this question isn’t about the core WooCommerce plugin – I’ll be marking it as solved.
I hope this helps!