How to handle orders for out-of-stock products on ecommerce site?

Dear community,

I regularly get orders with product that are out of stock.

I think these orders are placed a few days after the basket was put together. So customers receive an abandoned cart email. In this email, we link to the /Checkout page directly and not the /cart page.
This means that we do not refresh the cart page…Do you think this is the problem?

We did it this way because if we link to /cart in the abandoned cart email, we seem to lose the cart when the customer switch devices. What I would like to avoid…

Website is cool-simple.com

thanks a lot for your help!