Effects on SEO from temporary pages/listings
 

I wanted to get some input on how to do seo for a site that lets say is like a craigslist where people post listings but then after 5 months the listing disappears.

My worry is that the pages/listings being created will eventually get indexed and crawled by google but then after a few months when the listing expires and is deleted a problem may come up with search engine not being able to find page?

Would this be a potential problem?
How do listing sites like craigslist fix these sort of things?