The US has actually several emergency networks, a cellphone even without a valid sim card can still be used to dial 911 this is part of every cellular standard. But in more common cases when you are outside of the coverage of your carrier and with roaming disabled/no roaming partners you will still see Emergency/SOS displayed on your phone.

http://s9.postimg.org/umb1a3tjz/s5570.jpg

Besides 911 there are probably a few other emergency numbers in the US which are open on all cellphones, as well as the emergency broadcast system which will display push notifications on every modern cellphone in such cases as natural disasters.