Hello if there is not any room left in the overhead bin naturally you would have to check it but has anyone ever had to check a carry on and it became lost. Also would you have to go to baggage claim to get it ?
Not quite a direct answer to your question, but here's a thought: if there are fragile items in your carry-on, such as electronics, you would have the choice of putting the carry-on under the seat in front of you, in the event (as your question states) there was no room left in the overhead bins.
This of course reduces your leg-room on a long flight, but the trade-off would be avoiding the chance that fragile items would be damaged.
I have had this happen before, and the airline staff just did a gate check, where they took some people's larger carry ons at the gate. These bags were then retrieved right outside of the plane after the flight, not at the baggage claim.
Unfortunately, Leigh's experience is not universal though that's the way it's supposed to work. The last time my carry on was gate checked, I had to go to baggage claim to retrieve it. It was the ONLY bag there from the flight which was kind of strange.
Usually it's just the commuters that stick it in the jetway.
It can also be checked through to the final destination.
They'll tell you were it's going to be, regardless.
I have had them lose a gate-checked bag. However, when I have to gate check, I take virtually everything out of the suitcase and stuff it in an ultra lightweight zippered bag that I keep in my carry-on. Since it's unstructured, I can squeeze it in somewhere. That way I have everything essential, and I'm just checking a mostly empty suitcase. I've never had the airline object to this.
I have had some adventures with carry-on bags. I have had them gate checked and damaged beyond use; gate checked and never seen again; gate checked and pick up at the jetway; gate checked and pick up with the checked luggage. As far as I can tell, with my experience, there is no rhyme or reason to the process.
Last year I flew Condor from Seattle to Frankfurt. My bag was slightly over the 13 pound limit. I took out my computer (a 13 inch MacBook Air). My bag was under the limit. As I walked away from the check in personnel, I tucked my computer back into the bag as I had a long, long walk to the boarding gate. They actually ran after me and demanded that I take the computer out again and carry it by hand. I took it out again, frustratedly, and walked around a corner and put it back in again. At boarding they were there waiting at the gate, weighing carry-on bags again. By this time I had shifted some items from my tiny carry-on to my handbag, and I wasn't over the 13 pound limit. I felt a little paranoid about my bag. BTW, I was flying first class....