I’ve received a text from ‘Lost Mode’ saying it’s been turned off?

Sounds like a scam message - thieves trying to “phish” for credentials to get into the phone, or for your daughter to remove the phone from the list of devices associated with her Apple ID, so they can “make her phone their own.”

If your daughter’s phone was locked at the time it was stolen, with a hard to guess passcode that the thieves did not have a chance to learn, their chances of getting to see her data will be very slim and none even before it learns that it is Lost.

The thieves may be able to see whatever is in her Medical ID if she gave the phone permission to make that available when the phone is locked (for the benefit of first responders).

If your iPhone, iPad, or iPod touch is lost or stolen

If your iPhone or iPad is lost or stolen - Apple Support

Find My - Official Apple Support

Find My - Official Apple Support

If the battery has run down, or phone was powered off

the phone does not have an Internet connection where it is located

You cannot do anything if it is offline. Any remote erase requires the device be actively connected to the internet in order to receive remote commands.