I'm Miles from the Social Care team at Shopify.
Shipping costs are set by your supplier, not Shopify, so this question would be best directed to them. If your dropshipping, suppliers are able to change their shipping costs. You'll need to keep checking up on your products through your supplier to see if any of their pricing has changed.
If shipping is now being charged by your supplier, you may need to look at passing shipping costs to your customers, or even increasing the price of your products to cover the shipping costs. You can create price based shipping prices where customers need to spend a certain amount to unlock free shipping, or just charge a flat shipping rate for all customers. We have a great guide to help you plan your shipping strategy.
Please let me know if you have any questions at all!
Thanks so much for reaching back out to me.
It would certainly be a question you would need to raise directly with the supplier. As I mentioned in the above comment, suppliers may change their pricing from time to time, and it would be up to the merchant to adapt to those prices. This could look like adding a shipping cost for your customers, or even increasing the price of your products to absorb that shipping cost.
I'd love to be able to give you a better answer, but you would need to work out with your supplier a way for them to notify you of any changes to product or shipping costs.
In summary, suppliers are able to change their prices. This would reflect the cost of their business, along with many other factors. If you're not happy with them, your last option would be to try and find a new supplier who has the tools you need to run your business successfully.
Thanks again for reaching out to us. Good luck with your business!