This doesn't seem like the way this should work.  Am I doing something wrong?
I have attached images of the steps involved.  Sorry for the large images, but I thought that this would be the clearest way to communicate the problem.

because your cursor was still on the library file -  it's happened to me too.  Next time before deleting,  make sure you click on the item you want deleted else the last item you clicked will be deleted,  in this case,  you had the file selected and not the animation on the timeline. 
- you can see it on the 2nd image where the file is highlighted in green - meaning it was the current selection.

• My Spotify  My Twitter  My Twitch
  
• My NFT    My Marketplace My Blog
  
• Music Sync Licensing

☯🐉

"To define Tao is to defile it" - Lao Tzu

Hmm, I do not know how you managed to do that. Items from Smart Gallery cannot be deleted.
Beside the context menu you have shown is a timeline menu. Cutting from there should not do anything to the item regardless whether it is still selected or not.
If you can replicate it (I cannot), make a video and send it to Reallusion Feedback tracker. It is a bug as it seems.

I explicitly tried to deselect the item from my smart gallery in several different ways.  It is impossible to deselect.

After applying the animation to the character I click on the timeline to select it.  I then click on the timeline item to cut it.  I would think that the content item should be deselected when I click on the timeline item.

Ok, new information.  I don't even have to delete the timeline animation.  The moment I apply the animation from the smart gallery, it is removed.  As soon as I click away it is no longer accesable.

Sequence of events for clarity.

wow,  ok...that's different ( and scary ), and 4u2 is right,  it is unusual behavior -  I've seen how files can get accidentally deleted by having an incorrect selection but I've never seen the software delete files like that before, it's either a bug,  or possibly even something happening outside iclone altogether.   I can see several scenarios where files simply go missing that had nothing to do with iclone and everything to do with things ranging from security software,  to a failing drive to windows 10 updates being windows 10  -  if that's your operating system.
4u2ges is right,  this is something you want to present to the support staff - preferably with something they can recreate and see for themselves ....or maybe give them the project to see if it happens to them.

The only thing I'll suggest at this point is make sure you have a backup of at least your custom files and other things that can't be replaced from the RL store,  if it's windows 10 acting up - they have a history of wiping files with bugs.
Too many variables here to make any other suggestions and the Staff needs to see and confirm whats going on.

• My Spotify  My Twitter  My Twitch
  
• My NFT    My Marketplace My Blog
  
• Music Sync Licensing

☯🐉

"To define Tao is to defile it" - Lao Tzu

Ok, i'll do that.  Maybe this is related to my other problem with save files.  The computer and hard drive are brand new, only had it built about a week ago.  I haven't noticed any strange disk problems anywhere else yet, but i'll keep an eye out.

ironically enough failing drives on new computers  are not uncommon,  u never know if they are using refurbished parts,  or stocks of drives they bought in bulk that got smacked around in storage.    - Usually the 3 month mark is what gives you an idea if a drive is dependable. for example,  if your drive has bad sectors,  it makes sense that this is only happening to iclone if iclone is saving to damaged areas of the drive.  

You may want to rule this out by having your os fully check your drive for bad sectors - it takes a few hours so something like this you can do before going to sleep and wake up to see the results. - but also caution,  back up any important files before you do this, I've seen those drive tests reveal errors and delete a bunch of files in an attempt to fix those errors -  so you recover what you can while you still can before doing tests and repairs...i once had a friends drive completely crash on me while simply doing a checkdisk to see if it had problems,  the horror!!

Point being this is so unusual,  the importance of backing up can not be overstated.

• My Spotify  My Twitter  My Twitch
  
• My NFT    My Marketplace My Blog
  
• Music Sync Licensing

☯🐉

"To define Tao is to defile it" - Lao Tzu

Thank you very much.  I just ran chkdsk /r (which only took 20 minutes or so)
The issue I was having with save files seems to be resolved.  Maybe the others as well.

Going to have to do further tests to see what carnage has been wrought around my computer now.

Edit: it turns out that this problem is not resolved.  Items still deleted after applying them.