One diver's regulator fell off her mouthpiece, leaving her with nothing but a mouthpiece and no air. Instead of going to her buddy - who was right there - she bolted off to the surface.
Had exactly the same problem happen with an instabuddy on her first post cert dive. She got her cert in MN in a lake. We were at 50 ft in the ocean a month later and I was a stranger but in lead with her and her mother. Mouthpiece came off. She went for her spare reg but it was not where she expected to find it since it was in her pocket (rental gear) and not on her chest. I was about 8-10 ft away. She shot over to me and gave the OOA signal. Gave her my spare. Let her calm down. Located her spare and gave it to her. Once she was completely ok, we completed the dive with me staying close to her in case of another failure. Actually I did not have to worry about that. She was in remora mode.
So some of them are trained well and do react perfectly.
During the SI I explained that you can still breath off the reg and captain fixed her reg mouthpiece.
Mouth pieces coming off is a common problem that students should have stressed more. I know I had one come off in the first 20 dives I did.
As an aside I will comment that I was not a DM on this six pack. But I had let the daughter and equally newly trained mother I was buddying with quietly know that I was a DM. I feel that encourages them to come to me if there is an issue under water and helps with the first dive jitters. I had the option of going solo but felt that they could benefit from somebody with them and it turned out I was right.