Is there a way to rescue the contents of this messed up Fusion Drive?
Ok so I did a test before I tried it with the actual affected drive. I had an old 60 GB laptop spinning hard drive, and a 32 GB laptop-form-factor Corsair SSD, which I made into a Fusion Drive.
I first formatted each drive and did a secure erase in the process to make sure there were no retrievable files left on the drives. Then used the appropriate diskutil command to make the two into a 92 GB Fusion drive.



Then I copied my 76 GB Photos Library over to this drive, which will make sure there have to be files on both drives. Then left it to "simmer" for a while (i.e. left some time for Core Storage to move files and file blocks around), maybe 1 hour. Then I opened Photos with that library, deleted, duplicated and modified a few photos, maybe 10 or so, over about 15 minutes.

I know this is not a perfect representation of real world usage of a Fusion Drive over a long time, but I feel it would give me a reasonable true idea of the rescue potential of the files in a similar Fusion Drive setup.

Then the test: I properly unmount the Fusion Drive, then plug only the spinning hard drive back in. This replicates the problem with the iMac am I having, where the internal SSD went offline.
Now running the diskutil corestorage list command I see the exact same as I did with the iMac: the logical volume is there, but one of the physical disk is listed with no properties to show for it.

I then issue the diskutil cs delete command with the UUID of the logical volume (i.e.the Fusion Drive). It looks like diskutil is formatting the spinning hard drive as a normal HFS+ GUID partition disk, and after it's done the spinning hard drive appears on the desktop, seemingly empty, as you would expect.

Running Disk Rescue 4 on this disk with a Deep Scan shows me the the file rescue potential of this scenario is actually very good. DR4 is able to restore file names and folder structure of approximately 80% of the files and I end of with about 56 GB worth of images.

After this test I basically do the same with the actual iMac that I was tasked with, and I had pretty similar file rescue results with that internal 1 TB spinning hard drive.