As of right now, there is built in functionality to allow customers' to sort products by "product status" meaning that if you have in stock and out of stock items on your category page, you can make sure that all in stock items show before the out of stock ones.  However, for some reason, this same integration was never added to the search results page.  By default, the system seems to sort based on itemID or itemname, so if you have any out of stock items named in ASC order higher than the others, it will show first.  

I find benefit in leaving products displayed on the category pages that are out of stock to show customers' about upcoming products that might come back in and for SEO reasons.  Since this development already exists on the category pages, I feel that it would be a quick fix to simply apply it to the other catalog search template.