The phone must have a good Internet connection to be able to receive a request from Find My, like enabling Lost Mode or remotely erasing the phone.
Your phone might "updating" its location based on a Bluetooth signal picked up from other iPhones (this is the way that an AirTag works as well) but it will need a good cellular or Wi-Fi connection to enable Lost Mode, or if you want to erase the phone remotely.
If you see an "Offline" status on the phone, that means any one of the following is true at the time:
- The battery has run down
- The phone has been powered off....(most models)
- The phone does not have a good Internet connection
Obviously, there is nothing that you can do about this other than keep checking a few times each day to see if the status of the phone has changed.
Also keep in mind that iPhone thieves are very fond of placing a phone in a special type of small bag that will not allow the phone to either send or receive a signal. So, everything on the phone might be fine otherwise, but Find My will not be able to connect to the phone.
Be very careful if you see a message or email from "Apple" or "Apple Support" claiming that your phone has been found and they just need "a bit more information" to verify that the phone is yours and return it to you.
Anything like this that you see is a SCAM. You know this because Apple does not get involved with lost or stolen phones. As you have guessed, the message is from a bad guy who is trying to trick you into revealing personal information.
Ignore and delete any messages like this that you might see.