The product visibility in E-commerce website is normally connected to stock status. Yet there are specific areas to customize if you want to manage it more advanced.
In the shop, it can affect where products and/or ther prices are displayed to customers, e.g. product catalog, search results page, product detail page, wishlist(s), cross-selling, shopping cart and so on.
To control the product visibility, you can choose the rules implemented on a whole product category or a selected product individually or scope effected and based on stock status and rules.
To whom you want the product to be hidden from, e.g. to all visitors of the website, to specified group of customers like wholesale, retailer, VIP etc.
When does the product visibility rules begin and when does it end? This decision can combine with your sales & marketing strategy.
1) Product is still displayed but with message "Out of Stock" when your stock quantity of this product is below your minimum stock value
2) Product is still displayed but with no price available, and the possibility of adding to shopping cart and checkout is disabled. Of course you can add one option to let customer request quote from you
3) One extra note about product visibility in shopping cart, if the ordered quantity by customer is suddenly below the available stock quantity, make sure to provide sufficient and clear message to tell customer what is happening and how he/she can continue checking out or pre-order a certain amount of this selected product and wait it's available again.
For example, in following screenshot, customer just ordered 20 products and the available stock becomes 18, the checkout option then becomes impossible.
product visibility adapt
Now if the customer modifies the quantity to be lower than actual stock quantity, the error message is gone and checkout button is back.
If customer now tries to input more than available stock quantity, the quantity will be auto corrected to the largest available stock value (in this case, it is 18), also the error message to tell customer that his/her desired quantity is not available. Of course you can implement another process and flow to define what and how your customer can buy in such scenario based on your own business needs.
4) You can also display custom message based on the stock rules setup, e.g. "only 1 available" to create a sense of urgency.
Last but not the least, don't forget to handle situation of page not found or redirect customer to a set URL when you hide the whole category and someone tries to open it via direct url.
There are definitely more details and areas you can customize to make it both convenient to customers and achieve your specific business needs. If you have different business needs for product visibility, I'd like to hear more about it. :-)