What is the type of the site collection where the issue occurred ? Whether all 6000 site collections in the same web application?
Please follow below tips to troubleshoot the issue.
1.Go to central administration -> Monitoring -> Review job definitions -> Find Content Type Hub and Content Type Subscriber timer jobs -> Run now.
2.Go to that site collection -> Content type publishing under Site Collection Administration -> Tick “Refresh all published content types on next update”, then click “OK”.
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