note: this is not a feature request specifically linked to Garmin Connect but more to all the Garmin devices
If a runner/cyclist has a real emergency during training then he should normally have his legal id but in real life a lot of people don't have that with them while in most cases we all have our forerunner or edge with ourselves at that time. So it could be nice that our "In Case of Emergency" (ICE) numbers are listed on our Garmin device.
Technically this just means some clear text fields where we can put our full name, our ID number and an emergency phone number. And maybe the idea that this data automatically pops up flashing when an activity is stopped abrupt (no stop-button clicked but no further gps movement).
This might not save our lives but it might help in some cases and wouldn't it be a nice marketing stunt for Garmin that "your device saved your life" ;-)