SQL Server 2016 Restore Failure on DB Using Clustered Shared Volumes (Error 7627)
In Windows Failover Cluster 2016, you need to ensure all storage (except for node-local-tempdb) is configured as a dependent resource in the SQL Server cluster role.

In the example below, you can see this cluster has two disks, Disk_F and Disk_G; those are the only places where SQL Server will allow us to create data and log files for SQL Server.



When restoring a SQL Server 2005 database that has a full text catalog, you likely need to specify the location of the full-text catalog files, otherwise SQL Server will attempt to put them in the default location, which may not be on a cluster shared volume.  Use RESTORE FILELISTONLY FROM DISK = '\path\to\backup'; to determine the files that exist in the backup.  Ensure your restore statement has a MOVE clause for each file in the backup.

As a workaround, you might try restoring the SQL Server 2005 full-text-search-enabled database onto a non-clustered SQL Server 2016 instance, then take a backup of the database from the 2016 instance to restore onto the clustered 2016 instance.  I'm thinking it's possible there is a bug in the restore process for old full-text-enabled databases onto modern clustered instances.