It is just thread! Washing isn't going to hurt it, so just be gentle, wash by hand, dry flat. May require startch or liquid WSS to restiffen, but should be pretty easy. Linda

For sure, FSL is stitched onto WSS stabiliser which is then washed out, usually by soaking. Water isn't going to hurt it.
I'd be inclined to make a solution of washing detergent and warm water and let the napkin ring soak for a while. If the stain doesn't disappear easily then gentle squashing or patting between your hands might do the job. Difficult stains might need a pre-soak spray. With this much time in water you'll probably need to stiffen a napkin ring again.
Like Linda says, just be gentle.
AlmaG.

Sounds to me like we need to encourage you to do more FSL and actually use it yourself. There'd be way less people 'addicted' to doing FSL items if they weren't easily washable, I'm sure. Go for it. Maybe wash the whole lot of them and they would end up with a similar rate of softness to each other when done.

Zoe , you can hand wash FSL, and then dissolve your scraps of washaway or Solvey whatever you used to do your embroidery on ,dip your napkin rings into it to stiffen them again, then lay flat to dry

I am not sure that I would throw it in the washing machine - but hand washing will not hurt it - matter of fact - it might make it really soft and you might like it that way - but wash the rest of them at the same time - so they all have the same feel to them. Enjoy.

I had made some coasters and of course they ended up getting stained. I put them in a netting kind of cloth bag and threw them in the washing machine. Later dipped them into a solution made from WSS stabilizer scraps and water, layed them out to dry and they were good as new.