eCommerce Search and Product Availability

Hi all,

I am trying to locate any studies or papers that indicate how people
use search on an ecommerce site to determine the availability of a
product.

Our company is bouncing back and forth between two scenarios, and I am
looking for information that will sway it to the most relevant one.

Scenario 1: Person types in a search term. The site returns results.
Person then refines their search by size. Resulting page shows
everything in that size, including items that are sold out. Sold out
items show "sold out" next to item image.

Scenario 2: Person types in a search term. The site returns results.
Person then refines their search by size. Resulting page shows ONLY
things that are available for purchase in that size.

Would love to hear peoples thoughts (and if possible data to back up
the best scenario).

Thanks,
David