Microsoft SQL Server Metadata Corruption
Before you try any fixes, make sure you have backups.  


  unfortunately the warnings were ignored and they worked a week on the broken SQL database.


Use old backups to locate a version that does not have the corruption. You will need the most current corruption free backup as you work through the issue. 

Optimally you will take a fresh full backup, restore it to a test server, and try to work through the problem on the test server.  

When you make it worse than it was to begin with, restore the backup to your test server again and try again. 

Hopefully you have been taking regular backups (daily at least) if so make sure that old backups do not age out of the inventory, before you get the problem solved. 

If the data is highly valuable you might want to consider contacting a corruption consultant.