Shop have already deleted the Deleted the products from their Dashboard, however these deleted products can be searchable in Shop's customers cart and they can add to their cart as well.

If the Products are already deleted, they cannot be searchable anywhere so that customers cannot add these deleted products anyhow.

There is no error message there.

We have checked on our test account and deleted one product, however we can manually add the product in our customer's account as this deleted product is searchable and customer's can able to cart that deleted product.

We have asked the Shop to provide us the few SKU's of the items they already have deleted, we checked those Items in Shop's Dashboard and unable to find them, however these products are added in Shop's customer cart.

Product Name : snowman, C25193, #0225-PULL-SMPSFT-ICE