I can't think of a study off of the top of my head that could help you. What I can tell you is that if you are directing traffic to a page on your site, the content should be relevant to the search term. For example, you don't want to have a page for blue widgets attracting traffic for pink teddy bears. This will create an awful user experience, high bounce rate and decrease in traffic over time. As the engines see your page as less and less relevant and that it provides a bad user experience you will start to lose rankings.
However, there are exceptions to that logic. For example, I have a page on my site that is the landing page for a very popular product. The manufacturer discontinued the product and I didn't want to give up the value of the page, so I left the relevant content, added the discontinued text and then offered replacement models closer to the top of the page. If anyone happened to land on that page, I wouldn't lose the traffic, but instead give them relevant options. If I had changed the status to 404 or 410, then there would be no possibility of capturing or converting the traffic. Here is a page: http://www.apelectric.com/6241-Generac-Guardian-Series-14kW-p/6241.htm
I have also talked to lots of people who have websites with pages for events, community activities, concert pages and things of that nature. After the shows or events, the page doesn't necessarily have "purpose". The page can be used to aggregate reviews of bands or performers, community fairs. It can be used as a community forum, or it can simply be updated to offer upcoming schedules.
As far as out of stock products go, I wouldn't 404 or take down a page with an "out of stock" product. I don't know what platform you use, but Big Commerce gives me the option to add a "Pre-Order" button to a product when it goes out of stock. It would be optimal if your customers could still order a product if it is coming back into stock in the future. I would add a message near the add to cart button saying the item is temporarily out of stock, but you can order for shipment in the next 2-3 weeks, or however long the window of time is. The more information you give your searcher the more opportunity you are creating for engagement and conversions. 404ing the pages is not the answer to a short term inventory shortage. When you 404 or 410 a page you are running the risk of losing your ranking on that page, so when you enable the page again you will have to start ranking again. It could take time depending on the competition of the product.