SOS Fall alert didn't notify emergency contacts or EMS after a hard fall

Some research suggests that the Watch tries to be completely independent when sending Apple messages, typically using its own cellular connection if no Wi-Fi connection is available.

that said, it appears that to send an SMS message, SMS messages will be forwarded and sent through the iPhone's connection:

Make sure that your Apple Watch can connect to your iPhone, cellular, or Wi-Fi. To send and receive SMS/MMS from cellular models of Apple Watch, your paired iPhone must be powered on and connected to Wi-Fi or cellular, but your iPhone doesn’t need to be nearby.

from:

If you can’t send or receive messages on your Apple Watch - Apple Support

Perhaps your sister fell in a way that blocked the watch's cellular signals (such as watch underneath her body), and by the time it tried to send SMS messages, the phone was already in the snowbank and switched off.

<< it did show as a sent message in our conversation thread on my sister's iphone. Never appeared on my phone. >>

That suggests that possibly the iPhone died and failed to send (from either the watch or phone) then reverted to an SMS text message, and that did not go through.

I do not find it completely unusual that an Apple device sending an SMS text message never gets through. And when sent as an SMS message in a marginal area, I often get a notification that a message did NOT go through when the intend receiver assures me it did.

This compared to an Apple message which seems to virtually always go through.

Were the bubbles further back in that conversation BLUE bubbles, indicating Apple-to-Apple devices?

Did you configure iOS 26.2 to enable RCS messaging conversion to non-Apple phones? Wouldn't be necessary with mutual iPhones.

Settings > Apps > Messages > RCS Messaging > RCS Messaging (=⦿)

The iPhone will automatically dial emergency services after a severe crash, but it isn't clear if it will do so in a slip and fall incident, which it might treat differently than a crash incident. If not, you will need to manually initiate the SOS call. See Settings > Emergency SOS for more details.

author says this was Apple Watch alert.

That said, I wonder if their iPhone shutting off has some impact here.

I seem to recall that if the iPhone is nearby, its connection will be used preferentially, but I could be wrong.

Why was this an SMS message, in a green bubble?

are you not both Apple users (Blue Bubbles) ?

Was your sister in a marginal or SOS only or roaming signal area at the time of the fall ?