Q:

What happens when you remove (or lose) the SSD from a Fusion Drive? 

After storing data on a Fusion Drive, is it possible to downgrade your Mac to use the hard drive (HDD) by just removing the solid state drive (SSD)? 
In particular, I was wondering what happens when the SSD fails for one reason or another.  Under the hood, is a Fusion Drive's SSD just a clone of operating, system, applications and most used files?  If so, are all files safe on the old HDD and can it still boot?  Or do I need to format the HDD and reinstall operating system, every application and move files back to HDD? 

A:

The Fusion drive is an amalgam of the SSD and HDD.  If either piece gets removed or fails, you lose all the data.  It might be possible to retrieve some of it, but it would be a job for drive recovery experts. 
If you have a Fusion drive, it is possible to split it into the two separate pieces, resulting in a standard two-drive setup.  However this is a destructive process, you need to reinstall the OS and all your data afterwards, as well as the recovery partition.  On Macs that came with a pre-installed Fusion drive, you'll also run into issues where Disk Utility wants to "fix" the Fusion drive, so disk management needs to be done with the command line tools. 
If you really want to split your Fusion drive, make sure you have a backup — this will delete your data; then boot into the Recovery partition (⌘R on boot) and open Terminal. 
Run diskutil coreStorage list, and note the long string that appears after Logical Volume Group — that's the UUID.  Then run diskutil coreStorage delete UUID, replacing UUID with the actual string.  You can then reinstall OS X on the SSD or HDD and restore from a backup. 

A:

According to Anandtech's article Understanding Apple's Fusion Drive:

Total volume size is the sum of both parts.  In the case of the 128GB + 1TB option, the total available storage is ~1.1TB.  The same is true for the 128GB + 3TB option (~3.1TB total storage). 

If the total size of the storage is the size of the SSD plus the size of the HD, then the HD alone cannot hold all the data in the fusion drive.  Therefore, if you remove the SSD then you won't be able to continue to operate with just the HD. 

A:

If the SSD fails, the OS won't show you any files and you would need to send both drives to a recovery specialist and expect to get few to some files (and many fragments of files) back.  Since the tiered storage moves parts of files to the HDD, there is no guarantee the entire copy of a file will exist on either drive for recovery. 
Clearly a mostly full to the brim "Fusion Drive" will have many entire files moved to the HDD, but sadly, the things you use most are most likely to have some parts still on the SSD. 

You could swap a new drive in for the SSD and reconfigure the core storage (reformat the Fusion Drive) and restore from a backup (or not swap a new drive in but still reconfigure core storage and restore from a backup).  
Just like losing a drive from a RAID 1 stripe, you lose all data when Disk Utility "fixes" a broken Fusion Drive.  Having a full and up to date backup is extremely important for users of Fusion Drive.