So I sent an email to Yelp and they did actually respond several days later:
Hi there,
When a business is marked CLOSED on Yelp, it is automatically deprecated in search results, and will in time disappear from search results entirely.
The timing of that disappearance depends on factors such as the type of business and the metro it’s in. Generally a business will fall out of keyword or category search within a matter of a couple days, and name-specific searches within 9-12 months. That is, if Joe’s Bagels closes, it will fall out of search results for “bagels” sooner than it will for “Joe’s Bagels,” since the latter represents user intent to find that particular business and it makes sense to keep that info available for a longer time.
To prevent incorrect update submissions in the future and to stop users from suggesting that this listing be marked as open, our moderators have locked the fields. Unfortunately, we cannot control what appears in Google search results. Please remember that Google results change over time, so the content in question should eventually disappear.
For more information please visit our Support Center : https://biz.yelp.com/support-center/Yelp_Business_Page/Getting_Started/Why-does-Google-sometimes-show-content-from-Yelp-that-doesn-t-appear-on-Yelp-itself/en-US
Thanks!
Regards,
Andy
Yelp Support
San Francisco, California
Totally worthless as usual.