Secondary filegroup for Full Text Index only - rebuild when lost
(answering my own question)

OK, so we ran a simulation - what will happen if we lose the secondary filegroup file?

Not good.

The database gets stuck in recovery mode and you can't do anything about it - you can't set the "emergency" mode, you can't change it to "single_user" mode - nothing. Basically, every command you run throws an error Unable to open the physical file "xxx.mdf". Operating system error 2: "2 (The system cannot find the file specified.)

The only solution is to restore the database. But "rebuilding" a secondary filegroup won't work, even if there's only a fulltext index in it.