From Volusion's support article.
https://support.volusion.com/hc/en-us/articles/209957467-How-to-Use-the-Hide-When-Out-of-Stock-Option
How to Use the Hide When Out of Stock Option
When an order placed in your store causes the stock status of a product to drop to zero or below, your store will hide the product, provided the Hide When Out Of Stock setting (on the product's Advanced Info > Product Display tab) is set.
This will prevent the product from being viewed by customers on your store front until the product's stock value is incremented (either manually or through processing an RMA or purchase order). You can learn more about using the hide function by reviewing the Marking a Product as Hidden article.
Note that if any of your products have options for your customers to select from, you may wish to hide certain options when the associated product variant is out of stock, while leaving other options visible. The best way to automatically hide out-of-stock product options is by using Smart Match and the Inventory Control Grid.
Automatically Hiding When Out of Stock
Note that the Hide When Out Of Stock function only activates if the stock status of a product drops to zero or below due to a purchase. If you explicitly set the stock status to zero within a product's settings, it will not automatically trigger this setting. To manually hide a product from view on your store front, enable the Hide Product option within the Advanced Info > Product Display tab.
Furthermore, in order for products to automatically be hidden when out of stock, products need to be configured to not allow backorders. To do this, go to Settings > Config Variables and select the Checkout Variables. Make sure the Enable Back Orders check box is not selected. This will prevent Volusion from allowing any products at a stock less than 1 from being ordered and will allow the Hide When Out Of Stock variable to engage for all products.
If you have some products that you want to do this for and some you don't, you can set Enable Back Orders at a global level as described above but select the Do Not Allow Backorders check box for specific products under the Stock tab.
Note on Stock Value Updates
Briefly mentioned above, Volusion's Hide When Out Of Stock will inversely update products: Any product using this function will be automatically unhidden when the stock status for a product is updated to a positive quantity. Product stock can be updated manually from a product's settings page or automatically through the processing of an RMA or purchase order, or even through an import to your Volusion store's products table.
Also, please note that any product with Hide When Out Of Stock and Hide Product checked with a Stock Status set to Null (blank) or a positive value will be unhidden whenever any Stock Status is imported for any product in the store.
Please keep this function in mind when using this feature to prevent products you wish to remain hidden from being made available on your store front after product stock value updates.blockquote