Hi,
First check the option "Display out of stock products" of the HikaShop configuration. You want to have that option turned off so that products/variants without a stock won't be listed.
Now, suppose that you have a characteristic color and a characteristic size to a product. If you remove the blue/XL variant from the product, but that you have the blue/L and the red/XL variants, then on the product page, you'll still have blue and XL as these choices are needed in the dropdowns so that you can select blue/L and red/XL.
To avoid that, you can change the "characteristic selection method" to "list" in the HikaShop configuration, and in that case, instead of characteristic dropdowns, it will display a list of the available variants, which will prevent the possibility for the customer to see / select variants that do not exist.