What happens to hybrid hard disk (SSHD) when its SSD malfunction?

I have seen about 15 broken SSHD drives in the last 3 years myself (and heard of maybe another 20 cases from colleagues) and they all failed in the same way: Computer crashed because the disk just stopped working.
Pull the disk out and try to recover via another computer: Only garbage can be read or the disk refuses to work at all.

So forget about "degraded performance". It will simply die.
Expect significant (even 100%) data-loss and the entire device being a loss.

It makes sense:
SSDs, when they fail, do so, in most cases, completely. A classic HD might still be largely readable, except for the bad spots, but a SSD failure is usually 100% fatal causing 100% data-loss on the SSD.
There is usually no graceful warning that would allow the SSHD controller to move data from the failed SSD part to the still good HD.

And technically speaking a SSHD is just a JBOD build from a SSD and a HD, with some smart software on top that decides which data is best put on the SSD part and which on the HD part.
In terms of data-loss this is WORSE than loosing a single disk in any other JBOD configuration.
In a normal JBOD a lot of your files would be OK and recoverable. Only the ones on the bad disk and the ones straddling the disk-boundary would be lost.
However in a SSHD config your most-used files (and most of the folder-directly structure as that is frequently accessed too) will be on the SSD part (that is why you were using a SSHD in the first place). With that part gone there is in most cases not enough left to enable recovery.

This is actually a very astute question.

The manufacturers state simply it should be replaced. (Meaning it is dead once one part of it fails.)

From personal experience, once the SSD fails, you can't access the HDD. (1TB Seagate SSHD)

If you have the technical expertise to remove the memory from the HDD - you can replace it. BUT it isn't as easy as you might think, the data can get corrupted, you can static fry your drive. I did try that, as I had wasn't sure of the backup. I even considered swapping the actual disc platters to another identical drive.

Honestly, it's not worth the time for most of us to salvage a failing SSHD when you can get a newer, faster, bigger one for less than the cost of 1 hours labor. (I learned my lesson and just put a new 4TB SSHD into my box in anticipation of the 2TB failing)

If you know it's going out, insure your backups are up to date.

If it went out and there's stuff on it you really need - find a reputable data recovery service.