It would depend on how the coupon code was set up on Shopify, using their feature called "Discounts".
We recommend taking a close look at all of the discount codes you've created.
Technically yes, a customer can use a coupon code on a subscription product (but this would only work if you have it set up to apply to subscription products).
Most likely, you already have discount codes created in the past, and they have Shopify's default settings (which makes the discount code not apply to subscription products).
As a merchant, you'll have to manually opt-in and mark the discount code to apply to subscription products, if you want to have this functionality.
If you are worried that customers can use the discount code on top of a subscription discount and get a huge discount that was not intended, don't worry there are ways to make sure this does not occur.
If you do want to offer a discount code on a subscription product, Shopify lets you control every aspect of how this coupon code can be used.
Shopify normally defaults to the discount code not applying to subscription products.
Shopify lets you choose whether or not it's for one-time purchases and subscription products (all) or just subscriptions, or just one-time purchase products. It lets you choose specific products as well.
Shopify also let defaults to the discount being applied to the first order only and not all recurring charges.
Being able to control how the discount code is used on recurring charges is useful if you only want the customer to get a discount once on a subscription order, and not forever.
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