Quickly - some phone service providers use SIM Cards to store data on and identify phones with. These cards can be interchangeable with other phones offered by the same provider ( for instance AT&T). If you change cards between phones - the phone with your SIM card now is identified as being yours by the carrier. Verizon does not use this technology
So, what does that mean for you in terms of safety and using ICE?
If your phone is found on your person and the battery is expended but it is marked as having ICE Information inside then someone may be astute enough to retrieve the card and place it in a functioning phone - which is much more realistic than finding a spare battery somewhere that powers your phone. Phone numbers should be able to be retrieved using this method.
If you follow the E.123 Standard to list your contact names and numbers in your phone individually this will allow them to be viewed immediately in the phone being used to read your SIM Card.
If your contact numbers are stored in a folder in your phone there is a chance that a potentially lower-tech non folder capable phone could be used to read your card which will only display one of the numbers in your ICE folder(s) and not the others.
That could make a considerable difference and should be investigated with your current phone.
Check it out.