I'm on my third dipstick, this has happened to me twice before. I was lucky and was fairly confident that none had fallen/broken off in the tube. It's the plastic ball half way up the dipstick that would be more likely to break up and fall into the system imo. Twice i've managed to catch this part hanging from the dipstick ready to fall off.
As you describe the top part has broken off and hit the undertray as mine did.
If you haven't done the oil pick up pipe in the sump before, then maybe it's worth doing for long term peace of mind and preventive maintenance