Unable to save and error on DBCC CHECKDB
is it a physical or a virtual server? Please make a chkdsk on your filesystem where the database are stored. 

Please also try a BACKUP DATABASE with CONTINUE_AFTER_ERROR:

BACKUP DATABASE AdventureWorks2012   
 TO DISK = 'Z:\SQLServerBackups\AdvWorksData.bak'  
   WITH CHECKSUM, CONTINUE_AFTER_ERROR;  
GO  


More information about this here:

https://docs.microsoft.com/de-de/sql/relational-databases/backup-restore/specify-if-backup-or-restore-continues-or-stops-after-error

Regards,
Björn