Show products with no inventory

First of all, thanks for the great product.

I have a site that's selling sponsorships for an event. There are only 1 available in some categories, but I would like to display the sponsorship even when it's sold. When I change the quantity to zero, the product (sponsorship) no longer displays, which in most cases would be preferred. I'd like it to still show up with a quantity of zero, and then I would add some text to the description that would say "Purchased by Company Name" so that the company that purchased the sponsorship would get some extra visibility.

So my question is, can you display a product that's not available or has a quantity of zero?

Thanks for the quick response. I don't know how I missed that, but it's exactly what I needed.