Sharepoint 2013 Search- only one crawled item after full crawl

Suppose you have a Search service application provisioned in your Sharepoint 2013 site. Suddenly it stops providing search results.
The diagnostics shows:
- No errors in ULS
- No errors in crawl log
- Local Sharepoint Sites Content Source is pointed to hostname in Default AAM zone
- Crawler account has set a Full Read user policy in web application
- I'm able to login and browse the site using crawler account
BUT, a full crawl finished successful with a very suspicious result: only one item was crawled!

The reason is following: the MicrosoftSharePointTeamServices response header was missing in IIS site for default zone! The Central Administration site had that header, but application site hadn't. Normally each Sarepoint application's IIS site should have this header set after creation.
After adding the MicrosoftSharePointTeamServices header the full crawl finished successful with all site pages been crawled. The value of the header must be a current version of Sharepoint 2013 Server installed (including service packs).