My Mercruiser had the tips of the "saw blades" worn off from PO's sloppy shifting. I guarantee you it can and did jump out. Maybe jump out is the wrong term. Maybe slipped my not engaging and holding would be a better phrase.
On back and forth movement, there is movement caused by these same gears as the dog rides up and over the peak of the tooth then settles in the slot. Distance varies but it's like ?" give or take on my engines and new ones sitting at dealerships on new boats ready to sell that I checked just to ensure that mine was about right and not too much.
On the rubber hub slipping, once it breaks free, you have to cut the throttle and let it reengage. I had one prop (Turning Point Hustler) with a removable hub and looking at how that hub was built, brass star and plastic filler, seemed to me that it was a one time event. You smack something and if it didn't hold, it would shear and not reset like rubber does. What chapps me about the new hubs is that they are no better in that regard than the old days when OMC had the drive pins and every time you were in trouble and really needed some thrust, the damn thing would break (shear, hence the term shear pin) and you were without power........on the windward side of rip rap (where the fish feed) on a big body of water.................
All the above personal experiences and I feel that I understand the process!