I wanted to try to see a few of the old job listings that I had applied for via stack overflow careers but it doesn't appear that there is any way for me to see the listing once its taken down, I can only see my application. This seems like a useful feature to implement that wouldn't require much difficulty (single flag in the database for active/inactive listing and then soft deleting expired listings or moving them to another table so that they don't make the index for active listings have to sustain every listing every posted).
That's kinda actually how it works now. No job listing is ever deleted. They are just active or inactive. Inactive listings can only be seen by the owner or a Careers moderator (employees). Adding the functionality you're asking for would be a lot more work than you think.
It's a good suggestion though. I'll add it to the wishlist and hopefully we can add it in at some point.