I was a little shocked cycling my first 10 shots from my SA-22 when I erroneously thought that after 10, the bolt would be locked open. Not the case. However, unlike other .22 actions, I did read that firing on an empty chamber is not the same as with others and will not cause damage.
Neither my Remington Nylon 66 or Ruger Standard Model lock open after the last shot. Neither has suffered any damage after 30+ years with the occasional dry fire that results. I don’t make a habit of it though.